CurriculumGrade 12Mathematics

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

  1. Add (3 + 2i) + (5 − 7i).
  2. Multiply (1 + i)(1 − i).
  3. 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.

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En 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.

More Number & Quantity lessons

Quadratics with Complex SolutionsN-CN.C.7The Fundamental Theorem of AlgebraN-CN.C.9Finding Vector ComponentsN-VM.A.2Adding and Subtracting VectorsN-VM.B.4Representing Data with MatricesN-VM.C.6Matrix Addition and MultiplicationN-VM.C.8

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