Intro to the imaginary numbers
The imaginary unit
Pure imaginary numbers
Check your understanding
Simplifying pure imaginary numbers
|Unsimplified form||Simplified form|
|Original equivalence||Thought process|
|The square root of is an imaginary number. The square root of is , so the square root of negative is imaginary units, or .|
Let's practice some problems
Why do we have imaginary numbers anyway?
- With only the counting numbers, we can't solve ; we need the integers for this!
- With only the integers, we can't solve ; we need the rational numbers for this!
- With only the rational numbers, we can't solve . Enter the irrational numbers and the real number system!