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__Definition: __

In mathematics, a **complex number** is a number of the form .

Where a and b are real numbers, and i is the imaginary unit, with the property i^{ 2 }= −1. The real number *a* is called the *real part * of the complex number, and the real number *b* is the *imaginary part*. Real numbers may be considered to be complex numbers with imaginary part set to zero; that is, the real number *a* is equivalent to the complex number *a*+0*i*.

If *z = a + bi*, the real part (*a*) is denoted Re(*z*), and the imaginary part (*b*) is denoted Im(*z*).

Complex numbers can be added, subtracted, multiplied, and divided like real numbers. They cannot be ordered, but have other elegant properties.

__Equality:__

Two **complex numbers** are equal if and only if their real parts are equal and their imaginary parts are equal. That is, a + bi = c + di if and only if *a* = *c* and* b* = *d*.

__Notation and Operations:__

The set of all complex numbers is usually denoted by . Complex numbers are added, subtracted, and multiplied by formally applying the associative, commutative and distributive laws of algebra, together with the equation *i*^{2} = −1:

In order to add, substract, multiply or divide two complex numbers use our complex numbers calculator!