Argand Plane

Argand Plane

## Definition / Concept

A complex number $z=a+ib$ is represented by the point $(a,b)$ in a two-dimensional plane.

## Terminologies

- Real axis → Horizontal axis representing real parts.

- Imaginary axis → Vertical axis representing imaginary parts.

- Affix → Point representing a complex number in the Argand plane.

## Formula

For:

$$z=a+ib$$

the corresponding point is:

$$(a,b)$$

The distance from the origin is:

$$|z|=\sqrt{a^2+b^2}$$

## Conditions / Special Cases

If:

$$b=0$$

the point lies on the real axis.

If:

$$a=0$$

the point lies on the imaginary axis.

## Usage

- Used to visualize complex numbers geometrically.

- Used to solve locus and argument problems.