To the West..........- 1/2.........to the East...........1/2......to the South........- 1/2 i.....to the north 1/2 i....odd.......
Complex Plane
No, not that complex plane ... | |
... this complex plane: |
A plane for complex numbers!
|
(Also called an "Argand Diagram")
Real and Imaginary make Complex
A Complex Number is a combination of a Real Number and an Imaginary Number:
A Real Number is the type of number we use every day.
Examples: 12.38, ½, 0, −2000
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
12 = 1 × 1 = 1
02 = 0 × 0 = 0
What can we square to get −1?
?2 = −1
Squaring −1 does not work because multiplying negatives gives a positive: (−1) × (−1) = +1, and no other Real Number works either.
So it seems that mathematics is incomplete ...
... but we can fill the gap by imagining there is a number that, when multiplied by itself, gives −1
(call it i for imaginary):
(call it i for imaginary):
i2 = −1
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