1. Home
  2. Mathematics
  3. Complex Numbers
  4. Algebraic form

Algebraic form of a complex number

Allowed: constants, operators. To multiply use a*b not ab
In radians. Allowed: constants, operators. To multiply use a*b not ab

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,

graphic-representation-complex-number

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