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May 5th, 2012, 06:56 PM   #1
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How to deal with powers of i

While revising for my exam this week I came across a final problem in the set;

Express (-1+i)^i in the form a+ib

I have gotten until

2^(i/2).e^(-3pi/4)

However what should I do from here in order to bring the i down into standard form
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May 5th, 2012, 08:53 PM   #2
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Re: How to deal with powers of i

Use the identity:

and Euler's formula to get:



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May 5th, 2012, 10:36 PM   #3
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Re: How to deal with powers of i



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May 9th, 2012, 03:53 AM   #4
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Re: How to deal with powers of i

Here's a general solution to a complex number raised to a complex number:



Computing , the angle between the complex vector and the positive real axis, in radians, using the signs of and :









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