# How do you express the complex number in standard form: sqrt3(cos π/6 + i sin π/6)?

Aug 4, 2017

The standard form is $= \frac{3}{2} + \frac{\sqrt{3}}{2} i$

#### Explanation:

We need

$\cos \left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$

$\sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$

The complex number is

$z = \sqrt{3} \left(\cos \left(\frac{\pi}{6}\right) + i \sin \left(\frac{\pi}{6}\right)\right)$

Therefore,

$z = \sqrt{3} \left(\frac{\sqrt{3}}{2} + \frac{1}{2} i\right)$

$= \frac{3}{2} + \frac{\sqrt{3}}{2} i$