# Thread: quick question on complex no.s...I just need a start..

1. ## quick question on complex no.s...I just need a start..

hey there..
I have an assignment to submit early morning tomorrow..and I really want 2 get an idea about this problem..
it's on complex no.s
Evaluate:
(cosα +isinα)^4 / (sinα + icosα)^5

for the icos α part I want to ask.. what's the possible way to solve it?
Like shall I subtract the angle α from 90 degrees? ('pi over 2') or...?
I'd really appretiate ur help... just so I can start the question atleast..

2. For $\displaystyle (\cos\alpha+i\sin\alpha)^4$ use the Moivre formula $\displaystyle (\cos\alpha+i\sin\alpha)^n=\cos n\alpha+i\sin n\alpha$

For $\displaystyle (\sin\alpha+i\cos\alpha)^5$ use the formula $\displaystyle \sin\alpha=\cos\left(\frac{\pi}{2}-\alpha\right)$ and $\displaystyle \cos\alpha=\sin\left(\frac{\pi}{2}-\alpha\right)$ then the Moivre formula.

Then use $\displaystyle \displaystyle\frac{\cos\alpha+i\sin\alpha}{\cos\be ta+i\sin\beta}=\cos(\alpha-\beta)+i\sin(\alpha-\beta)$