Graphing of Complex Numbers

The complex number consists of a real part and an imaginary part, which can be considered as an ordered pair (Re(z), Im(z)) and can be represented as coordinates points in the euclidean plane. The euclidean plane with reference to complex numbers is called the complex plane or the Argand Plane, named after Jean-Robert Argand. The complex number z = a + ib is represented with the real part – a, with reference to the x-axis, and the imaginary part-ib, with reference to the y-axis. Let us try to understand the two important terms relating to the representation of complex numbers in the argand plane. The modulus and the argument of the complex number.

Modulus of the Complex Number

The distance of the complex number represented as a point in the argand plane (a, ib) is called the modulus of the complex number. This distance is a linear distance from the origin (0, 0) to the point (a, ib), and is measured as r = |√a2+b2a2+b2|. Further, this can be understood as derived from the Pythagoras theorem, where the modulus represents the hypotenuse, the real part is the base, and the imaginary part is the altitude of the right-angled triangle.