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Complex Plane
Advanced


No, not that complex plane .




Imaginary
+i


Real
0
... this complex plane: −1 0 1


−i

A plane for complex numbe



(Also called an "Argand Diagram")




Real and Imaginary make Complex
A Complex Number is a combination of a Real Number and an Imaginary Num




A Real Number is the type of number we use every day.


Examples: 12.38, ½, 0, −2000



When we square a Real Number we get a positive (or zero) result:


22 = 2 × 2 = 4
12 = 1 × 1 = 1
02 = 0 × 0 = 0


What can we square to get −1?

, imaginary2 negative.

Examples: 5i, -3.6i, i/2, 500i



And together:




A Complex Number is a combination of a Real Number and an Imaginary


Examples: 3.6 + 4i, −0.02 + 1.2i, 25 − 0.3i, 0 + 2i




Putting a Complex Number on a Plane
You may be familiar with the number line :



-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 1


But where do we put a complex number like 3+4i ?


Let's have the real number line go left-right as usual, and have the imaginary
number line go up-and-down:




5i
Imaginary


4i
3i
We can then plot a complex number like 3 + 4i : 2i
3 units along (the real axis), i
and 4 units up (the imaginary axis).
0
-4 -3 -2 -1 0 1
-i
-2i
-3i
-4i
ry




5i