Multiplying Complex Numbers
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State
Complex numbers multiply by distribution, with i² replaced by −1 wherever it appears.
Show
(2 + 3i)(1 + 4i) runs FOIL: 2 + 8i + 3i + 12i² = 2 + 11i − 12 = −10 + 11i.
Watch for
The i² step is where the arithmetic turns.
Builds on
- Nothing — this is a starting point.
Unlocks
- Nothing yet depends on this.