Square Roots of Negative Numbers
This video presents the same text shown beside it, spoken and on screen. It adds nothing the text does not say.
State
The principal square root of a negative number is imaginary: √(−a) = i√a for positive a.
Show
√(−9) = 3i, and the check squares back: (3i)² = 9i² = −9. The radical now answers every real input.
Watch for
Factor the −1 out as i before touching anything else.
Builds on
- Nothing — this is a starting point.
Unlocks
- Nothing yet depends on this.