Why is $\frac 25$ the real part of $\frac{1}{2+i}$? According to Wolfram Alpha, Re(1/(2+i))=2/5.  
How did it calculate that?

$\frac{1}{a+bi}=\frac{1}{a+bi}\frac{a-bi}{a-bi}=\frac{a}{a^2+b^2}+i\cdot bla$
$a=2,b=1\implies \frac{a}{a^2+b^2}=\frac{2}{2^2+1^2}=\frac{2}{5}$
