Question

Z=32(cos(n/3) + isin(n/3)

Answer 1

Recall that

$\bf r[cos(\theta )+i~sin(\theta )]\quad \begin{cases} x=rcos(\theta )\\ y=rsin(\theta ) \end{cases}\implies (x,y)\\\\ -------------------------------$

therefore,

$\bf Z=\stackrel{r}{32}\left[cos\left( \stackrel{\theta }{\frac{n}{3}} \right)+i~ sin\left( \stackrel{\theta }{\frac{n}{3}} \right)\right]\qquad \begin{cases} r=32\\ \theta =\frac{n}{3} \end{cases}\implies \begin{cases} x=32cos\left( \frac{n}{3} \right)\\\\ y=32sin\left( \frac{n}{3} \right) \end{cases} \\\\\\ \left[ 32cos\left( \frac{n}{3} \right)~~,~~ 32sin\left( \frac{n}{3} \right)\right]$