Okay. Find the integral solution of $$ (1-i)^n =2^n $$

I just want to know who's to do this which is explained in as many steps as possible. Thanks in advance.

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    $\begingroup$ It's not possible to give an explanation in as many steps as possible, sorry. Given an explanation, there exists another explanation with more steps. $\endgroup$ – David C. Ullrich Oct 6 '15 at 14:08
  • $\begingroup$ @David C. Ullrich: Is that an Incompleteness theorem for explanations ? $\endgroup$ – Bernard Oct 6 '15 at 14:13
  • $\begingroup$ Okay. Just explain to me the basic idea as to how I can solve this question. $\endgroup$ – Giridhar Oct 6 '15 at 14:14
  • $\begingroup$ @Bernard Why, I suppose it is. I'm gonna be famous. Godel, Church, Turing, Ullrich... cool. $\endgroup$ – David C. Ullrich Oct 6 '15 at 14:21
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    $\begingroup$ @Giridhar Hint: Write $1+i$ in the form $re^{i\theta}$. $\endgroup$ – David C. Ullrich Oct 6 '15 at 14:21

$$\begin{align} |(1-i)^n| &= |2^n|\\ |1-i|^n &= |2|^n\\ (\sqrt2)^n &= 2^n \end{align}$$

The only potential solution is $n=0$

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