# How do you express the complex number in trigonometric form  2(cos 90° + i sin 90°)?

##### 1 Answer
Jul 30, 2015

In a sense, it's already in trigonometric form. Other common ways to write it, which may be what you are after, are $2 \setminus m b \otimes \left\{c i s\right\} \left({90}^{\circ}\right)$ and $2 {e}^{i \cdot {90}^{\circ}} = 2 {e}^{i \cdot \frac{\pi}{2}}$.

#### Explanation:

The second form follows from Euler's formula: ${e}^{i \theta} = \cos \left(\theta\right) + i \sin \left(\theta\right)$.

The "cis" form of the answer is just another way to write it ($m b \otimes \left\{c i s\right\} \left(\theta\right)$ is a symbol that is, by definition, equal to $\cos \left(\theta\right) + i \sin \left(\theta\right)$).

All of this can also be thought of in terms of polar coordinates in the complex plane. The polar coordinates of the complex number $2 \left(\cos \left({90}^{\circ}\right) + i \sin \left({90}^{\circ}\right)\right) = 2 i$ are $\left(r , \theta\right) = \left(2 , {90}^{\circ}\right)$ (its rectangular coordinates are $\left(x , y\right) = \left(0 , 2\right)$).