Trignometry Function 517

Question

Use DeMoivre 's Theorem to find the indicated power. Write the answers in rectangular form.
 
[√2(cos pi/4+i sin pi/4)]^-8
 
Please show step by step work to solution and provide final answer. Please and Thank You!

Answer 1

In DeMoivre's Theorem, the exponent becomes a multiplier of the theta value within the "sin θ + isin θ"part, and of course is used as an exponent over the r part.  

 

This gives 2^-4 (sin (-2pi) + i cos (-2pi) = (1/16)(0 +1i ) =i/16.