Question

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

Answer 1

B

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.