Question

how do I write 0.0462-0.369i in polar form using the exponential form

Answer 1

mostly a calculator exercise

Answer 2

\[ 0.0462-0.369i =r\left(\cos(\theta)+i\sin(\theta)\right)\]
\[r=\sqrt{a^2+b^2}=\sqrt{(0.0462)^2+(0.369)^2}\]

Answer 3

and \[\tan(\theta)=\frac{b}{a}=-\frac{0.369}{.0462}\] making \[\theta=\tan^{-1}(-\frac{0.369}{.0462})\]