SOLUTION: (cos45+isin45)^8

Question 420878: (cos45+isin45)^8
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The easy way to raise a complex number to a power is DeMoivre's Theorem:
For any complex number

then

For your complex number, , there is no visible r. So the r must be a 1. Writing your expression with a visible r we get:

Now we can use DeMoivre's Theorem to rewrite your expression:
1^8(cos(8*45) + i*sin(8*45))
which simplifies as follows:
1(cos(360) + i*sin(360))
1(1 + i*0)
1(1)
1
So (cos45+isin45)^8 = 1
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