#### What are complex numbers?

A complex number can be written in the form a + b*i* where a and b are real numbers (including 0) and *i* is an imaginary number

Therefore a complex number contains two 'parts':

- one that is real
- and another part that is imaginary

**note:**Even though complex have an imaginary part, there are actually many real life applications of these "imaginary" numbers including oscillating springs and electronics.

**Examples** of a complex number

$$ \begin{array}{c|c} \blue 3 + \red 5 i & \\\hline \blue{12} + \red{\sqrt{-3}} & \red{\sqrt{-3}} \text{ is } \blue{imaginary} \text{ part} \\\hline \blue 9 - \red i & \\\hline \blue{12} - \red{\sqrt{-25}} & \red{\sqrt{-25}} \text{ is } \blue{imaginary} \text{ part} \\\hline \end{array} $$

#### How do you graph complex numbers?

Complex numbers are often represented on a complex number plane (which looks very similar to a Cartesian plane).

- On this plane, the imaginary part of the complex number is measured on the 'y-axis', the vertical axis
- the real part of the complex number goes on the 'x-axis', the horizontal

**Practice **Problems of complex number

This complex number is in the fourth quadrant.

This complex number is in the 2nd quadrant.

This complex number is in the 3rd quadrant.