Lorena T.

asked • 12/08/23

nth distinct root

How do I show (1+i)^n = -9 algebraically and graphically.

I figured out that polar form form 1+i. Not sure what to do with -9

sqrt 2^p(cos (p⋅45°)+ i sin (p⋅45°).

please show work


Mark M.

tutor
Are you sure that (1 + I)^n = -9 and not -4? If n = 4, then, by DeMoivre's Theorem, (1 + I)^4= (sqrt2)^4[cos180 + isin180] = 4(-1 + 0i) = -4.
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12/09/23

1 Expert Answer

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Mark M. answered • 12/09/23

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Well I calculated the powers of 1 + i from 2 through 8 and none of them result in -9.

Please check your post for accuracy.

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Lorena T.

Question was given by teacher. Can you show share your solution.
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12/09/23

Mark M.

tutor
Are you sure that the equation is (1+I)^n = -9 and not -4? By DeMoivre's Theorem, (1+I)^4 = (sqrt2)^4[cos180 + isin180] = 4(-1 + 0i) = -4.
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12/09/23

Lorena T.

I got the same answer. I'm not sure why the teacher would ask a question that has no solution.
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12/09/23

Brenda D.

tutor
Lorena T did you ask the teacher about this question relative to Mark M’s information above? Is it possible that there is a typo in the question? Is it possible that no solutions is the answer?
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12/16/23

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