Question

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

Convert the polar form of the complex number to its equivalent rectangular form

Answer 1

z = 16 + 16i√3

Answer 2

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