# MandysNotes

## The Pythagorean Theorem from Euler’s Formula

14 May 2011

Consider any complex number $z, \$with modulus

$\sqrt{z\bar{z} } = |z| = r \ ,$

where $r \in \mathbb{R^{+}}\ .$

Note that $\frac{z}{r} \$would be a complex number with modulus one:

$| \frac{z}{r} | = | \frac{z}{|z|} | = 1.$

## The Pythagorean Theorem

04 September 2009