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
picture of complex plan and cartesian plane
Diagram of Graph of Complex Numbers

PracticeProblems of complex number

Problem 1

Identify the coordinates of all complex numbers represented in the graph below.

Identify Complex Numbers on Graph
Problem 2

In what quadrant, is the complex number $$ 2- i $$ ?

This complex number is in the fourth quadrant.

picture of graph of two minus i
Problem 3

In what quadrant, is the complex number 2i -1?

This complex number is in the 2nd quadrant.

picture of graph of two i minus 1
Problem 4

In what quadrant, is the complex number $$-i -1 $$ ?

This complex number is in the 3rd quadrant.

picture of graph of  -i minus 1
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