Imaginary unit
Graphic representation

The complex numbers can be represented graphically by drawing the real number line as the horizontal axis and the imaginary numbers as the vertical axis of a Cartesian plane called the complex plane. In this representation, the numbers 1 and i are at the same distance from 0, with a right angle between them. Addition by a complex number corresponds to translation in the plane, while multiplication by a unit-magnitude complex number corresponds to rotation about the origin. Every similarity transformation of the plane can be represented by a complex-linear function z ↦ a z + b. {\displaystyle z\mapsto az+b.}
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