- #1
Gregg
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- 0
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
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