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is the answer for this n=4k? (k is an integer)
 

Etho_x

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I think it's correct.

If you convert 1 - i and 1 + i to Euler form, you will find that 1 - i has an argument of -pi/4 and 1 + i has an argument of pi/4. Both have a mod of sqrt(2).

We want the real part, meaning Im(z) = 0.

The only way this can be done is if you have multiples of 4, since if you take n = 0, 4, 8... and convert into polar form, the imaginary part (isinx) will be 0.

Typing this on the fly so haven't properly been able to work it out but I think your answer's correct.
 

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