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## Homework Statement

Evaluate [itex] Re[(a+bi)^p] [/itex]

## The Attempt at a Solution

[itex](a+bi)^p =\sum _{k=0}^p \left(

\begin{array}{c}

p \\

k

\end{array}

\right) a^{p-k} (\text{bi})^k[/itex]

[itex]Re[(a+bi)^p] =\sum _{k=0}^p \left(

\begin{array}{c}

p \\

k

\end{array}

\right) a^{p-k} (\text{bi})^k [/itex]

[itex]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}[/itex]

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

Last edited: