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Multiplying and Dividing Complex Numbers
Master multiplying complex numbers with the FOIL method and dividing them using the complex conjugate, with worked examples that show every step.
What You'll Learn
Apply the FOIL method to multiply two complex numbers of the form a plus bi and c plus di
Simplify any i squared term to negative 1 to finish a complex number multiplication
Recognize the complex number multiplication formula ac minus bd plus ad plus bc times i
Multiply by the complex conjugate to remove i from a denominator when dividing complex numbers
Calculate the denominator of a complex division problem as c squared plus d squared after conjugation
Compare multiplying and dividing complex numbers to rationalizing a denominator with a square root
What You'll Practice
1
Multiplying binomial complex numbers and simplifying using i² = -1
2
Multiplying complex numbers with radicals and mixed terms
3
Dividing complex numbers using conjugate multiplication
4
Simplifying products of conjugate pairs to eliminate imaginary parts
Why This Matters
Multiplying and dividing complex numbers is essential for advanced algebra, engineering, and physics. You'll use these skills when solving quadratic equations with no real solutions, analyzing electrical circuits, and working with waves and oscillations in calculus and beyond.
Before You Start — Make Sure You Can:
This Unit Includes
8 Video lessons
Practice exercises
Learning resources
Skills
Complex Numbers
FOIL Method
Conjugates
i² = -1
Simplification
Division
Imaginary Numbers
IL Curriculum Aligned