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

**KAS** · November 11th 2008, 06:52 AM

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..

**red_dog** · November 11th 2008, 07:26 AM

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

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

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

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