# Complex numbers

#### What are complex numbers?

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

Therefore a complex number contains two 'parts':

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

### Examples of a complex number

• $$3 + 5 i$$
• $$12 + \sqrt{-3}$$ ($$\sqrt{-3}$$ is the imaginary part)
• $$4 +22i$$
• $$11 - i$$
• $$12 - \sqrt{-125}$$ ($$\sqrt{-125}$$ is the imaginary part)

#### 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 part is measured on the 'y-axis', the vertical axis
• the real part goes on the 'x-axis', the horizontal

### PracticeProblems 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.

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