# How do you write the complex number in standard form 3.75(cos((3pi)/4))+isin((3pi)/4))?

Aug 31, 2016

$3.75 \left(\cos \left(\frac{3 \pi}{4}\right) + i \sin \left(\frac{3 \pi}{4}\right)\right) = - 2.652 + i 2.652$

#### Explanation:

As $\cos \left(\frac{3 \pi}{4}\right) = - \frac{1}{\sqrt{2}}$ and $\sin \left(\frac{3 \pi}{4}\right) = \frac{1}{\sqrt{2}}$

$3.75 \left(\cos \left(\frac{3 \pi}{4}\right) + i \sin \left(\frac{3 \pi}{4}\right)\right)$

= 3.75(-1/sqrt2+i×1/sqrt2)

Now as $\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ above is equal to

$3.75 \left(- \frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2}\right)$

= -(3.75×sqrt2)/2+i(3.75×sqrt2)/2

= -(3.75×1.4142)/2+i(3.75×1.4142)/2

= $- 2.652 + i 2.652$