Find All Complex Number Solutions z=i

This is the trigonometric form of a complex number where ${\displaystyle \left|z\right|}$ is the modulus and ${\displaystyle \theta }$ is the angle created on the complex plane.

The modulus of a complex number is the distance from the origin on the complex plane.

Substitute the actual values of ${\displaystyle a=0}$ and ${\displaystyle b=1}$.

Pull terms out from under the radical, assuming positive real numbers.

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

Since the argument is undefined and ${\displaystyle b}$ is positive, the angle of the point on the complex plane is ${\displaystyle \frac{\pi }{2}}$.

Substitute the values of ${\displaystyle \theta =\frac{\pi }{2}}$ and ${\displaystyle \left|z\right|=1}$.