# How do you write the complex number in standard form [3/2(cos(pi/2)+isin(pi/2))][6(cos(pi/4)+isin(pi/4))]?

Nov 2, 2016

$- 9 \frac{\sqrt{2}}{2} + 9 \frac{\sqrt{2}}{2} i$

#### Explanation:

Given:

$\left[\frac{3}{2} \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right)\right] \left[6 \left(\cos \left(\frac{\pi}{4}\right) + i \sin \left(\frac{\pi}{4}\right)\right)\right] =$

Multiply the magnitudes and add the angles:

$9 \left(\cos \left(\frac{3 \pi}{4}\right) + i \sin \left(\frac{3 \pi}{4}\right)\right) =$

To obtain standard form, you evaluate the trig functions and use the distributive property with the magnitude:

$- 9 \frac{\sqrt{2}}{2} + 9 \frac{\sqrt{2}}{2} i$