Question

Given the complex number z=6(cos120+isin120), find z3

Answer 1

Answer:

B

Step-by-step explanation:

We are given the complex number:

$\displaystyle z = 6(\cos 120^\circ + i\sin 120^\circ)$

And we want to find z³.

Recall that:

$\displaystyle z^n = r^n(\cos(n\theta) + i\sin (n\theta))$

In this case, n = 3. Hence:

$\displaystyle z ^3 = (6)^3 (\cos (3(120^\circ)) + i\sin (3(120^\circ))$

Simplify:

$\displaystyle z^3 = 216(\cos 360^\circ + i\sin 360^\circ)$

Evaluate:

$\displaysyle z^3 = 216( 1 + i(0)) = 216$

In conclusion, our answer is B.