Re[ (a+bi)^p]

Homework Statement

Evaluate $Re[(a+bi)^p]$

The Attempt at a Solution

$(a+bi)^p =\sum _{k=0}^p \left( \begin{array}{c} p \\ k \end{array} \right) a^{p-k} (\text{bi})^k$

$Re[(a+bi)^p] =\sum _{k=0}^p \left( \begin{array}{c} p \\ k \end{array} \right) a^{p-k} (\text{bi})^k$

$Re[\displaystyle \sum _{k=0}^p \text{bi}^k a^{p-k} \left( \begin{array}{c} p \\ k \end{array} \right)] = \sum _{k=0}^{p/2} \left( \begin{array}{c} p \\ 2k \end{array} \right) a^{p-2k} (\text{bi})^{2k}$

I just thought that for each even power of bi that that part will be real. The answer is completely different though. Just confused.

http://www.exampleproblems.com/wiki/index.php/CV8

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