The complex plane is a two-dimensional model that allows for the easy conceptualization of complex numbers, the prime icon of those being the imaginary number, the square root of -1. Each complex number can be thought of as a point in the plane (or as a vector extending from the origin to that point).
The horizontal axis of the complex plane is identified with the real number line and the vertical axis with the imaginary number line.
Thus, the first coordinate of a point in the complex plane represents the real part of the corresponding complex number and the second coordinate the imaginary part. This is called rectangular form.
Additionally, complex numbers within the complex plane can be described much like polar coordinates, with an argument and modulus. The important identity Euler's formula relates complex numbers in exponential form to rectangular form.
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