# Complex plane

## Geometric representation of the complex numbers / From Wikipedia, the free encyclopedia

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In mathematics, the **complex plane** is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called the **real axis**, is formed by the real numbers, and the vertical y-axis, called the **imaginary axis**, is formed by the imaginary numbers.

The complex plane allows for a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed more easily in polar coordinates—the magnitude or *modulus* of the product is the product of the two absolute values, or moduli, and the angle or *argument* of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation.

The complex plane is sometimes called the **Argand plane** or **Gauss plane**.