### Complex number

A complex number is represented by algebraic notation as

The set of complex numbers is denoted by the symbol **C**.

##### Explanation

A complex number corresponds with a point in the complex plane. It consists of the real numbers *a* and *b*, and is written as

The *a* is a real number and *bi* is an imaginary number. It can normally be used in calculations.

Every real numbers is also a complex number, because *x* = *x + *0*i*. Also *i* itself is a complex number, because *i = *0 + 1*i*. The real numbers are then *a = *0 and *b = *1. The imaginary unit *i* has only an imaginary part, and has therefore no real value.

##### Complex plane

The complex plane is a geometric representation of complex numbers, and consists of a real *x*-axis and orthogonaly the imaginary *y*-axis.