# How do you write the complex number -3+4i in polar form?

Nov 15, 2016

The polar form is =5(cos126.9º+isin126.9º)

#### Explanation:

Let $z = a + i b$ a complex number

The polar form is $z = r \left(\cos \theta + i \sin \theta\right)$

$r = \sqrt{{a}^{2} + {b}^{2}}$

Here, we have $z = - 3 + 4 i$

$\therefore r = \sqrt{9 + 16} = \sqrt{25} = 5$

$z = 5 \left(- \frac{3}{5} + \frac{4 i}{5}\right)$

$\therefore \cos \theta = - \frac{3}{5}$ and $\sin \theta = \frac{4}{5}$

So, $\theta$ is in the second quadrant

$\theta = 126.9$º

z=5(cos126.9º+isin126.9º)