Argand Plane

A complex numbers \(x+iy\) can be plotted in cartesian coordinate as the point \((x,y)\). This plane is called Argand plane.

Addition and Substraction¶

Addition and substraction of complex numbers in Argand plane are similar to the vector addition and multiplication.

1. Multiplication in Complex Numbers¶

If we multiply two complex number \(z_1=r_1e^{i\theta_1}\) and \(z_2=r_2e^{i\theta_2}\), then we get

Hence in polar coordinate, the magnitude will get multiplies while angle will get added.

2. Sequence and Series in Complex Numbers¶

Similar to real sequance, a complex sequence in simple a function \(f: \mathbb{N} \to \mathbb{C}\).

Example of a diverging sequence.