Question

Review the graph. Given z = , which letter represents z3? A B C D

Answer 1

By writing Z in polar form, we will see that:

$z^3 = C$

How to get the value of Z³?

First, we can see that:

z = (-1 - i)

If we write it in polar form, we get:

$z = \sqrt{2} *e^{i(\pi + \pi/4)$

If we apply the power 3, we get:

$z^3 = (\sqrt{2} *e^{i(\pi + \pi/4)})^3\\\\z^3 = 2^{3/2}*e^{i*(3\pi + 3\pi/4)}\\\\z^3 = 2^{3/2}*e^{i*15\pi/4}$

Notice that:

$\frac{15\pi}{4}$

Is an angle equivalent to:

$\frac{15\pi}{4} - 2\pi = \frac{15\pi}{4} - \frac{8\pi}{4} = \frac{7\pi}{4} = 1.75\pi$

Because the angle is measured from the positive x-axis, this means that we will have:

$z^3 = C$

If you want to learn more about complex numbers:

brainly.com/question/10662770

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