Complex Number as a Vector

Complex Number as a Vector

## Definition / Concept

The complex number:

$$z=a+ib$$

can be represented by the vector:

$$\vec z=a\hat i+b\hat j$$

## Formula

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

The sum of complex numbers corresponds to vector addition:

$$z_1+z_2\leftrightarrow\vec z_1+\vec z_2$$

## Usage

- Used to connect complex-number problems with coordinate geometry and vector interpretation.