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Question

How does the complex plane work?


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Solution

Complex plane or argand plane :

The complex plane (also called the Argand plane or Gauss plane) is a way to represent complex numbers geometrically. It is basically 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.

Complex number represented: z=x+iy

Example:

z=3+2i, where x and y are real numbers, and i is the imaginary unit. In this customary notation the complex number z corresponds to the point x,y in the Cartesian plane.

Hence, the complex plane is basically a modified Cartesian plane where the xx-axis and the yy-axis have been dubbed the "real axis" and the "imaginary axis," respectively.


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