Answer
$z^3$
= $- 23.38 + 13.50i$ (corr. to 2 decimal places)
Work Step by Step
$z = 3(cos50^\circ + isin50^\circ) = 3cis50^\circ$
Now, $z^3$
= $(3cis50^\circ)^3$
= $3^3 cis 3\cdot 50^\circ$ (De Moivre’s Theorem)
= $27cis150^\circ$
= $27(cos150^\circ + isin150^\circ)$
= $27(-\frac{\sqrt{3}}{2} + \frac{1}{2} i)$
= $-\frac{27\sqrt{3}}{2} + \frac{27}{2}i$
= $- 23.38 + 13.50i$ (corr. to 2 decimal places)
