Explain why is real for all Thanks in advance for any help
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Hello, Originally Posted by janvdl Thanks in advance for any help Note that and Then let n=4k, 4k+1, 4k+2, 4k+3, and use properties of exponents. If you're stuck... well you know what to do
you have a simple case of . remember Bobak
Originally Posted by bobak you have a simple case of . remember Bobak And this is especially clear if you consider the polar form of 1 + i and 1 - i and then raise each to the power of n using de Moivre's Theorem.
Finally, you could do this using the binomial theorem, together with the fact that , and combining all odd powers of i.
Last edited by HallsofIvy; January 11th 2009 at 10:44 AM. Reason: Edited thanks to Opalg
Originally Posted by HallsofIvy Finally, you could do this using the binomial theorem, together with the fact that , and combining all odd powers of i. ... but preferably don't use i as an index in a question about complex numbers.
Originally Posted by Opalg ... but preferably don't use i as an index in a question about complex numbers. lol! Or j .....
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