SOLUTION: I am given z=(5.5+5.5i);determine z^4 I multiplied it all out and used i^1=i, i^2=-1, i^3=-i, i^4=1. I got -14660.283 and its not right. Any help?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I am given z=(5.5+5.5i);determine z^4 I multiplied it all out and used i^1=i, i^2=-1, i^3=-i, i^4=1. I got -14660.283 and its not right. Any help?      Log On


   

Question 258433: I am given z=(5.5+5.5i);determine z^4
I multiplied it all out and used i^1=i, i^2=-1, i^3=-i, i^4=1. I got -14660.283 and its not right. Any help?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I am given z=(5.5+5.5i);determine z^4
z = 5.5(1+i)
Using multiplication:
z^4 = (5.5^4)*(1+i)^4
z^4 = 915.0625*(2i)^2
z^4 = -4*915.0625
z^4 = -3660.25
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|z| = 5.5*sqrt(2)cis(45)
z^4 = (5.5^4)*4cis(180)
z^4 = 3660.25*(-1 + 0)
z^4 = -3660.25