How do you express the complex number in trigonometric form: 3?

Jun 27, 2016

$3$ is written as $3 \cos 0 + i \sin 0$ or $3 {e}^{i 0}$

Explanation:

A number $a + i b$ is written as $r \cos \theta + i r \sin \theta$ or $r {e}^{i \theta}$ in polar form,

where $r = \sqrt{{a}^{2} + {b}^{2}}$ and $\tan \theta = \frac{b}{a}$

As $3 = 3 + i 0$, r=sqrt(3^2+0^)=sqrt9=3

and as $\tan \theta = \frac{0}{3} = 0$, $\theta = 0$

Hence $3$ is written as $3 \cos 0 + i \sin 0$ or $3 {e}^{i 0}$