Mathematics: Given z^2=1/2(cos(2pi/5)+i sin(2pi/5)), which lettered point represents z?

Given z^2=1/2(cos(2pi/5)+i sin(2pi/5)), which - id212252510052555, savage5447

Ответ:

tragicteekaay

14.02.2022

is represented by point A.

Step-by-step explanation:

According to the De Moivre's Formula, the power of a complex number of the form $z = r\cdot (\cos \theta + i\,\sin \theta)$ is defined by this formula:

$z^{n} = r^{n}\cdot [\cos n\theta + i\,\sin n\theta]$ (1)

Where:

- Norm of the complex number, dimensionless.

$\theta$ - Direction of the complex number, measured in radians.

- Power of the resulting complex number, dimensionless.

Given that $z^{2} = \frac{1}{2}\cdot \left[\cos \left(\frac{2\pi}{5} \right)+ i\,\sin \left(\frac{2\pi}{5} \right)\right]$ , then the following variables are: