Question

Simplify the following expressions and write the results in the polar form re iθ . ( √ 3 + i ) ^5

Answer 1

can you write it by using equation facility?

Answer 2

your job is to write \(\sqrt{3}+i\) in trig (polar) form
do you know how to do that?
you need two numbers, \(r\) and \(\theta\) to write \(a+bi\) as \(re^{i\theta}\)
\(r=\sqrt{a^2+b^2}\)

Answer 3

in your case \(r=\sqrt{\sqrt{3}^2+1^2}=\sqrt{3+1}=\sqrt{4}=2\)

Answer 4

as for \(\theta\) you can sometimes use \(\theta=\tan^{-1}(\frac{b}{a})\)
if you are in quadrant 1 or 4
in your case you get \(\theta=\tan^{-1}(\frac{1}{\sqrt{3}})\)

Answer 5

do you know that number?