trigo with complex number

Algebra Level 2

$\cos π/4+i\sin π/4$

can be written as

e^{iπ/4}

iπ/4

e

\sqrt{2}

1 solution

Melissa Quail
Jan 11, 2015

According to Euler's formula:

$e^{ix} = cos x + i sin x$

In this question we have $cos \frac{π}{4} + i sin \frac{π}{4}$ so $x=\frac{π}{4}$ and therefore

$cos \frac{π}{4} + i sin \frac{π}{4}$ = $\boxed{e^{\frac{iπ}{4}}}$