then
![\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.](/tpl/images/0330/2444/39bb1.png)
![z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;](/tpl/images/0330/2444/4a5e8.png)
![z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};](/tpl/images/0330/2444/bf499.png)
![z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;](/tpl/images/0330/2444/f6d56.png)
![z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};](/tpl/images/0330/2444/3d765.png)
![z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;](/tpl/images/0330/2444/7f8ba.png)
![z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};](/tpl/images/0330/2444/d3020.png)
![z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;](/tpl/images/0330/2444/436ad.png)
![z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};](/tpl/images/0330/2444/4065e.png)
-i
i
1 + i
Mathematics, 18.10.2019 03:50 kingsavage2002
Which of the following is not one of the 8th roots of unity?
-i
i
1 + i
√2/2 + √2/2 i
Answers: 1
Another question on Mathematics
Mathematics, 22.06.2019 01:30
Write 37/22 as a decimal rounded to the nearest hundredth.
Answers: 1
Mathematics, 22.06.2019 03:20
Indicate the equation of the given line in standard form. the line containing the longer diagonal of a quadrilateral whose vertices are a (2, 2), b(-2, -2), c(1, -1), and d(6, 4).
Answers: 2
Mathematics, 22.06.2019 03:30
Acone is placed inside a cylinder. the cone has half the radius of the cylinder, but the height of each figure is the same. the cone is tilted at an angle so its peak touches the edge of the cylinder’s base. what is the volume of the space remaining in the cylinder after the cone is placed inside it?
Answers: 1
Mathematics, 22.06.2019 03:30
Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about y = 8.8y = x3, y = 0, x = 4use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the given curves about y = 8.8y = x3, y = 0, x = 4
Answers: 1
You know the right answer?
Which of the following is not one of the 8th roots of unity?
-i
i
1 + i
-i
i
1 + i
Questions
Mathematics, 22.04.2020 20:05
Mathematics, 22.04.2020 20:05
Mathematics, 22.04.2020 20:05
Geography, 22.04.2020 20:05
English, 22.04.2020 20:06
Biology, 22.04.2020 20:06
Social Studies, 22.04.2020 20:06
