SOLUTION: The expression(-1+i)^3 is equivalent to (1) -3i (2) -2-2i (3) -1-i (4) 2+2i ----------- ----------- ----------- ----------- ----------- ----------- ---------- please choose

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The expression(-1+i)^3 is equivalent to (1) -3i (2) -2-2i (3) -1-i (4) 2+2i ----------- ----------- ----------- ----------- ----------- ----------- ---------- please choose       Log On


   

Question 233419: The expression(-1+i)^3 is equivalent to
(1) -3i
(2) -2-2i
(3) -1-i
(4) 2+2i
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please choose the correct answer choice and explain how to get the answer
Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The expression(-1+i)^3 is equivalent to
(1) -3i
(2) -2-2i
(3) -1-i
(4) 2+2i
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(-1+i)^2 = 1-1 - 2i = -2i
(-1+i)^3 = -2i*(-1+i) = 2i + 2
= 2+2i --> #4
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-1+i = sqrt(2)cis135
(-1+i)^3 = 2sqrt(2)cis405
= 2sqrt(2)cis45
= 2sqrt(2)*(cos(45) + isin(45))
= 2 + 2i Same answer