# How do you write the complex number in trigonometric form 3-i?

Feb 18, 2017

The answer is =sqrt10(cos(-18.4º)+isin(-18.4º))

#### Explanation:

The trigonometric form of a complex number

$z = a + i b$

is

$z = r \left(\cos \theta + i \sin \theta\right)$

$r \cos \theta = a$

$r \sin \theta = b$

${r}^{2} = {a}^{2} + {b}^{2} = | z {|}^{2}$

Here, we have

$z = 3 - i$

$r = | z | = \sqrt{9 + 1} = \sqrt{10}$

$z = \sqrt{10} \left(\frac{3}{\sqrt{10}} - \frac{i}{\sqrt{10}}\right)$

$\cos \theta = \frac{3}{\sqrt{10}}$

$\sin \theta = - \frac{1}{\sqrt{10}}$

So, we are in the fourth quadrant

$\theta = - 18.4$º

z=sqrt10(cos(-18.4º)+isin(-18.4º))