Expansion of imaginary numbers If $(1+i)^{100}$ is expanded, what is the value of the real part of the result? I know that this has to do with binomial theory and Pascal's triangle, but I don't know how to use it here.

Instead of expanding the term $1+i$, let's write it in polar for as $2^{1/2}e^{i\pi/4}$.
Then, we have 
$$(1+i)^{100}=2^{50}e^{i25\pi}=-2^{50}$$
