Operations with Complex Numbers
Aligned to N-CN.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Add and subtract complex numbers by combining real parts and imaginary parts separately. Multiply by using the distributive property, then replace i^2 with −1.
Worked example
Multiply (2 + 3i)(4 − i). Distribute: 2×4 + 2×(−i) + 3i×4 + 3i×(−i) = 8 − 2i + 12i − 3i^2. Since i^2 = −1, −3i^2 = +3, giving 8 + 3 + 10i = 11 + 10i.
Practice questions
- Add (5 − 2i) + (−3 + 6i).
- Subtract (7 + i) − (4 − 3i).
- Multiply (1 + i)(1 − i).
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Operaciones con Números Complejos
Suma y resta números complejos combinando por separado las partes reales y las partes imaginarias. Multiplica usando la propiedad distributiva y luego reemplaza i^2 por −1.
Ejemplo: Multiplica (2 + 3i)(4 − i). Distribuye: 2×4 + 2×(−i) + 3i×4 + 3i×(−i) = 8 − 2i + 12i − 3i^2. Como i^2 = −1, −3i^2 = +3, resultando 8 + 3 + 10i = 11 + 10i.
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