Adding and Multiplying Complex Numbers
Aligned to N-CN.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Treat the imaginary unit i like a variable, but replace i^2 with −1. Add complex numbers by combining real and imaginary parts; multiply by distributing (FOIL).
Worked example
Multiply (2 + 3i)(1 − 4i) = 2 − 8i + 3i − 12i^2 = 2 − 5i − 12(−1) = 2 − 5i + 12 = 14 − 5i.
Practice questions
- Add (3 + 2i) + (5 − 7i).
- Multiply (1 + i)(1 − i).
- Simplify (2 − 3i)(4 + 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
Sumar y multiplicar números complejos
Trata la unidad imaginaria i como una variable, pero reemplaza i^2 por −1. Suma números complejos combinando las partes reales e imaginarias; multiplica distribuyendo (FOIL).
Ejemplo: Multiplica (2 + 3i)(1 − 4i) = 2 − 8i + 3i − 12i^2 = 2 − 5i − 12(−1) = 2 − 5i + 12 = 14 − 5i.
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