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Complex Plane Definition

The complex plane otherwise known as the argand plane, z-plane or gauss plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis. In simpler terms, it is a coordinate plane used to graph complex numbers. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis. Accordingly the x-axis is called the real axis and the y-axis is called the imaginary axis.

The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers can be expressed most easily in polar coordinates which is 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. Multiplication by a complex number of modulus 1 acts as a rotation.

Related Definitions

Sources

“Complex Plane.” Wikipedia, Wikimedia Foundation, 28 Apr. 2020, en.wikipedia.org/wiki/Complex_plane.

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