Complex numbers as vectors Geometric Representation

A complex number $c= a+ib$ corresponds to a point in the $XY$-plane. If we call the $X-$axis as Real axis and the $Y-$ axis as imaginary axis the new plane will be called complex plane.

Every complex number $c= a+ib$ corresponds to a point $(a, b)$ in the Complex plane.

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Also every complex number $c= a+ib$ can be viewed as a vector.

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If $\bf {v} = (a,b)$ represents complex number $c= a+ib$, then length of this vector is called absolute value or modulus of the complex number $c= a+ib$.