Question

Suppose z = . What is z4? on EDGE 2020

Answer 1

Answer:

$z^{4} = \cos \frac{8\pi}{3}+i\,\sin \frac{8\pi}{3}$

Step-by-step explanation:

We can determine the power of a complex number by the De Moivre's Theorem, which states that for all $z = r\cdot (\cos \theta + i\,\sin\theta)$, where $a, b \in \mathbb{R}$, the power of the complex number is:

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

Where:

$r$ - Magnitude of the complex number, dimensionless.

$\theta$ - Direction of the complex number.

If we know that $r = 1$, $n = 4$ and $\theta = \frac{2\pi}{3}$, then the fourth power of the complex number is:

$z^{4} = 1^{4}\cdot \left[\cos\left(\frac{8\pi}{3} \right)+i\,\sin\left(\frac{8\pi}{3}\right)\right]$

$z^{4} = \cos \frac{8\pi}{3}+i\,\sin \frac{8\pi}{3}$

Answer 2

Answer:

ITS B ON EDGE

Step-by-step explanation: