# Algebraic form of a complex number

Convert a complex number from the exponential form to its algebraic form.

## Graphic representation

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

The polar and exponential forms of z are written,`z = r *( cos(\varphi) + i * sin(\varphi)) = r * e^(i*\varphi)`

r = |z| is the modulus from z.

`\varphi` is the argument from z.

## Algebraic form

The algebraic form of z is written,`z = x + i * y`

So we have,

`x = r * cos(\varphi)`

`y = r * sin(\varphi)`

## See also

Modulus of a complex number

Argument of a complex number