This section provides step-by-step examples on how to perform operations with complex numbers in both rectangular (standard) and polar forms. You will learn how to handle the imaginary unit $i$, perform arithmetic on complex numbers, find roots using De Moivre's theorem, and interpret them geometrically on the Argand plane.

The foundation of complex numbers is the imaginary unit $i$, defined as the principal square root of $-1$ ($i = \sqrt{-1}$).

The standard form of a complex number is $a + bi$, where $a$ is the real part and $b$ is the imaginary part. Operations are performed by treating $i$ as a variable and applying $i^2 = -1$.

Complex numbers can be represented by a magnitude ($r$) and an angle ($\theta$) in the complex plane. This is written as $r(\cos \theta + i\sin \theta)$ or $r e^{i\theta}$ using Euler's formula.