# Exponential and polar forms of a complex number

This tool converts a complex number from the algebraic format (a + b.i) to its exponential and polar forms.

## Graphic representation

z is a complex number represented by the point M on the plane of complex numbers as follows,## Polar form

The polar form of z is written,`z = r *( cos(\varphi) + i * sin(\varphi))`

r = |z| is the modulus of z.

`\varphi` is the argument of z.

## Exponential form

The exponential z format is written,`z = r * e^(i*\varphi)`

## See also

Modulus of a complex number

Argument of a complex number