Distance Between Two Complex Numbers

Distance Between Two Complex Numbers

## Formula

If $z_1$ and $z_2$ represent two points in the Argand plane, then the distance between them is:

$$|z_1-z_2|$$

If:

$$z_1=x_1+iy_1,\qquad z_2=x_2+iy_2$$

then:

$$|z_1-z_2|=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$

## Conditions / Special Cases

Distance is always non-negative:

$$|z_1-z_2|\ge0$$

The distance is zero if and only if:

$$z_1=z_2$$

## Usage

- Used in geometric interpretation and locus problems involving complex numbers.