Question

Solve the complex variable equation (-9/2)*sqrt(3) + (9/2)*i
So that it is in the form ______*exp(i_______)

Answer 1

you need two numbers \(r\) and \(\theta\)
\(r=\sqrt{a^2+b^2}\) which in your case is
\[\sqrt{\left(-\frac{9\sqrt3}{2}\right)^2+\left(\frac{9}{2}\right)^2}\]

Answer 2

then \(\theta\) find via \(\sin(\theta)=\frac{b}{r}\) and \(\cos(\theta)=\frac{a}{r}\)
sometimes you can use \(\theta =\tan^{-1}(\frac{b}{a})\) but not in this case because you are in the second quadrant