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1.  Compute
 

[ (1-i)^10(sqrt3 + i)^5 ] / (-1-i*sqrt3)^10

 

 

2. 

Find the real part of (sqrt3 - i)^2011

 

 

3. Let z = 3[cos(85) + i*sin(85)]. Find the smallest positive value of r such that r[cos(45) + i*sin(45)] = z^n for some positive integer n. 

 Dec 25, 2022
 #3
avatar+33337 
+1

Here's number 1:

 

Try a similar approach for the others.

 Dec 26, 2022

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