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1.6进一步的复数

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1 1 b 1 c 2 2 b 2摄氏度 3 3 b 3 c 3 d 4 4 b 4摄氏度 4 d 5 5 b 6 6 b 6摄氏度 7一个 7 b 7 c 8

问题1

分数:2

考虑w=z1z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W = z下标1 / z下标2" style="vertical-align:-23px;height:59px;width:56px">,在那里z1=2+23i{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1 = 2 + 2√3 I" style="vertical-align:-12px;height:32px;width:101px">而且z2=2+2i.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标2等于2加2i。" style="vertical-align:-12px;height:28px;width:79px">

(一)
表达w{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="w" style="vertical-align:-6px;height:22px;width:15px">在表格中w=a+bi{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W = a + b I" style="vertical-align:-6px;height:22px;width:73px">．

    评估你的分数
    关键概念
    复数共轭和除法
    笛卡尔形式

    问题1 b

    分数:2
    (b)
    写出复数z1{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">而且z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标2" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">在表格中reiθ, r≥0, -π<θ<π{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="R e的I次幂末端指数，空格R大于等于0，空格- < (<" style="vertical-align:-6px;height:23px;width:162px" loading="lazy">．
      评估你的分数
      关键概念
      模量和参数
      指数(欧拉)形式

      问题1 c

      分数:2
      (c)
      表达w{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="w" style="vertical-align:-6px;height:22px;width:15px" loading="lazy">在表格中reiθ, r≥0, -π<θ<π.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="R e的I次幂末尾指数，空格R大于等于0，空格- < (<)" style="vertical-align:-6px;height:23px;width:167px" loading="lazy">
        评估你的分数
        关键概念
        指数(欧拉)形式

        问题2

        标志:4

        考虑这个等式z4-1=15{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z的4 - 1次方等于15" style="vertical-align:-6px;height:23px;width:78px" loading="lazy">,在那里z∈ℂ{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="直复数的Z元素" style="vertical-align:-6px;height:22px;width:38px" loading="lazy">．

        (一)
        找出方程的四个不同的根，在表格中给出答案a+bi{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A + b I" style="vertical-align:-6px;height:22px;width:42px" loading="lazy">,在那里a,b∈ℝ.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A, b个实数元素。" style="vertical-align:-6px;height:22px;width:59px" loading="lazy">
          评估你的分数
          关键概念
          二次方程的复根
          笛卡尔形式

          问题2 b

          分数:2
          (b)
          表示下面阿根图(a)部分中的根。


          q8b_1-9_ib-maths-aa-hl
            评估你的分数
            关键概念
            根图

            问题2摄氏度

            分数:2
            (c)
            求顶点由阿根图上的四个根表示的多边形的面积。
              评估你的分数
              关键概念
              根图

              问题3

              标志:4

              让z1=6 cis(π6){"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="开始mathsize 16px样式z下标1 = 6c I s左括号直PI / 6右括号结束样式" style="vertical-align:-15px;height:39px;width:87px" loading="lazy">而且z2=32eiπ4.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="开始mathsize 16px style z下标2等于3根号2 e的I次方右括号右括号除以4结束指数。结束的风格" style="vertical-align:-11px;height:40px;width:105px" loading="lazy">

              一)
              在表格中给出答案rcisθ,{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="rcs，逗号" style="vertical-align:-6px;height:22px;width:42px" loading="lazy">找到

              (我)
              z1z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1 Z下标2" style="vertical-align:-12px;height:28px;width:33px" loading="lazy">

              (2)
              z1z2.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="开始mathsize 16px样式z下标1 / z下标2。结束的风格" style="vertical-align:-22px;height:55px;width:28px" loading="lazy">
                评估你的分数
                关键概念
                模-参数(极坐标)形式
                指数(欧拉)形式

                问题3 b

                分数:2
                b)
                写z1{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">而且z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标2" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">在表格中a+bi.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A + b i。" style="vertical-align:-6px;height:22px;width:47px" loading="lazy">
                  评估你的分数
                  关键概念
                  形式转换

                  问题3 c

                  分数:2
                  c)
                  找到z1+z2,{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1 + Z下标2，逗号" style="vertical-align:-12px;height:28px;width:55px" loading="lazy">在表格里给出你的答案a+bi.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A + b i。" style="vertical-align:-6px;height:22px;width:47px" loading="lazy">
                    评估你的分数
                    关键概念
                    模-参数(极坐标)形式
                    形式转换

                    问题3 d

                    分数:2

                    已知z1*{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1上标星号乘以" style="vertical-align:-13px;height:30px;width:19px" loading="lazy">而且z2*{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标2上标星号乘以" style="vertical-align:-13px;height:30px;width:19px" loading="lazy">的复共轭吗z1{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">而且z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标2" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">分别。

                    d)
                    找到z1*+z2*,{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1上星号乘以+ Z下标2上星号乘以逗号" style="vertical-align:-13px;height:30px;width:59px" loading="lazy">在表格里给出你的答案a+bi.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A + b i。" style="vertical-align:-6px;height:22px;width:47px" loading="lazy">
                      评估你的分数
                      关键概念
                      复数共轭和除法
                      复杂的加法，减法和乘法

                      问题4

                      分数:2

                      让z1=2 cis(π3){"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="开始mathsize 16px样式z下标1等于2 c I s左括号直PI / 3右括号结束样式" style="vertical-align:-15px;height:39px;width:87px" loading="lazy">而且z2=2+2i{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="开始mathsize 16px样式z下标2 = 2加2直I结束样式" style="vertical-align:-11px;height:26px;width:65px" loading="lazy">．

                      一)
                      表达

                      (我)
                      z1{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">在表格中a+bi{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A + b I" style="vertical-align:-6px;height:22px;width:42px" loading="lazy">

                      (2)
                      z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标2" style="vertical-align:-12px;height:28px;width:17px" loading="lazy">在表格中r cisθ{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="rcs" style="vertical-align:-6px;height:22px;width:40px" loading="lazy">

                        评估你的分数
                        关键概念
                        形式转换

                        问题4 b

                        分数:2
                        b)
                        找到w1=z1+z2,{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W下标1 = z下标1 + z下标2，逗号" style="vertical-align:-12px;height:28px;width:93px" loading="lazy">在表格里给出你的答案a+bi{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A + b I" style="vertical-align:-6px;height:22px;width:42px" loading="lazy">．
                          评估你的分数
                          关键概念
                          复杂的加法，减法和乘法

                          问题4摄氏度

                          分数:3
                          c)
                          找到w2=z1z2,{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W下标2 = z下标1 z下标2，逗号" style="vertical-align:-12px;height:28px;width:76px" loading="lazy">在表格里给出你的答案r cisθ.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="rcs。" style="vertical-align:-6px;height:22px;width:45px" loading="lazy">
                            评估你的分数
                            关键概念
                            模-参数(极坐标)形式

                            问题4 d

                            分数:2
                            d)
                            草图w1{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W下标1" style="vertical-align:-12px;height:28px;width:22px" loading="lazy">而且w2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W下标2" style="vertical-align:-12px;height:28px;width:22px" loading="lazy">在一个阿根图上。
                              评估你的分数
                              关键概念
                              根图

                              问题5

                              分数:3

                              已知z1=2eiπ3{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1等于2e的I次方右括号是/ 3右括号是尾指数" style="vertical-align:-11px;height:36px;width:72px" loading="lazy">而且z2=3 cis(nπ12), n∈ℤ+.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标2等于3c s左括号分数分子n正的PI除以分母12结束分数右括号逗号空格n个正整数的正次方元素。" style="vertical-align:-15px;height:41px;width:150px" loading="lazy">

                              一)
                              找到…的价值z1z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1 Z下标2" style="vertical-align:-12px;height:28px;width:33px" loading="lazy">为n=3.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="N = 3。" style="vertical-align:-6px;height:22px;width:42px" loading="lazy">
                                评估你的分数
                                关键概念
                                模-参数(极坐标)形式

                                问题5 b

                                分数:3
                                b)
                                求的最小值n{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="n" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">这样z1z2∈ℝ+.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1个Z下标2个正数的正次方。" style="vertical-align:-12px;height:29px;width:77px" loading="lazy">
                                  评估你的分数
                                  关键概念
                                  模-参数(极坐标)形式
                                  根图

                                  问题6

                                  分数:5

                                  考虑复数w=z1z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="开始mathsize 16px样式w = z下标1 / z下标2结束样式" style="vertical-align:-22px;height:55px;width:52px" loading="lazy">在哪里z1=3-3i{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1等于3减去根号3i" style="vertical-align:-12px;height:32px;width:92px" loading="lazy">而且z2=2 cis2π3.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="开始mathsize 16px style z下标2 = 2c I s开括号分数分子2直PI /分母3结束分数闭括号。结束的风格" style="vertical-align:-15px;height:41px;width:104px" loading="lazy">

                                  一)
                                  表达w{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="w" style="vertical-align:-6px;height:22px;width:15px" loading="lazy">在表格中r cisθ.{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="rcs。" style="vertical-align:-6px;height:22px;width:45px" loading="lazy">
                                    评估你的分数
                                    关键概念
                                    形式转换
                                    模-参数(极坐标)形式

                                    问题6 b

                                    分数:3
                                    b)
                                    草图z1, z2{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z下标1，空格Z下标2" style="vertical-align:-12px;height:28px;width:42px" loading="lazy">而且w{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="w" style="vertical-align:-6px;height:22px;width:15px" loading="lazy">在下面的阿根图上。

                                    q6b_1-9_ib-maths-aa-hl

                                      评估你的分数
                                      关键概念
                                      根图

                                      问题6摄氏度

                                      分数:2
                                      c)
                                      求的最小正整数值n{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="n" style="vertical-align:-6px;height:22px;width:11px" loading="lazy">这样wn{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W的n次方" style="vertical-align:-6px;height:23px;width:23px" loading="lazy">是实数。
                                        评估你的分数
                                        关键概念
                                        模-参数(极坐标)形式
                                        根图

                                        问题7

                                        标志:4

                                        考虑复数w=3cosπ3-isinπ3{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="W = 3开括号cos / 3 - isin / 3闭括号" style="vertical-align:-17px;height:44px;width:162px" loading="lazy">而且z=3-3i{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="Z = 3 -根号3i" style="vertical-align:-6px;height:26px;width:85px" loading="lazy">．

                                        (一)
                                        写w{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="w" style="vertical-align:-6px;height:22px;width:15px" loading="lazy">而且z{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="z" style="vertical-align:-6px;height:22px;width:10px" loading="lazy"> 在表格中r cis θ{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="R空间cis空间" style="vertical-align:-6px;height:22px;width:46px" loading="lazy">,在那里r>0{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="R > 0" style="vertical-align:-6px;height:22px;width:33px" loading="lazy">而且-π<θ≤π{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="负的直线小于，小于或等于" style="vertical-align:-6px;height:22px;width:79px" loading="lazy">．
                                          评估你的分数
                                          关键概念
                                          模-参数(极坐标)形式
                                          模量和参数

                                          问题7 b

                                          分数:2
                                          (b)
                                          求的模和模zw{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="z w" style="vertical-align:-6px;height:22px;width:23px" loading="lazy">．
                                            评估你的分数
                                            关键概念
                                            模-参数(极坐标)形式

                                            问题7 c

                                            分数:2
                                            (c)
                                            写下的值zw{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="z w" style="vertical-align:-6px;height:22px;width:23px" loading="lazy">．
                                              评估你的分数
                                              关键概念
                                              模-参数(极坐标)形式

                                              问题8

                                              分数:5

                                              写5cos2t+3+4 cos2t+5{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="5cos(开括号)2t + 3(闭括号)加上4space cos(开括号)2t + 5(闭括号" style="vertical-align:-6px;height:22px;width:194px" loading="lazy">在表格中Acos2t+B{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="acos，开括号2t加上B，闭括号" style="vertical-align:-6px;height:22px;width:96px" loading="lazy">在哪里A>0, -π<B<π{"language":"en","fontFamily":"Times New Roman","fontSize":"18"}" class="Wirisformula" role="math" alt="A大于0，空格减去小于B的直线" style="vertical-align:-6px;height:22px;width:135px" loading="lazy">．

                                                评估你的分数
                                                关键概念
                                                三角函数的频率与相位
                                                形式转换


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