MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

MathLabwith Mr. Ahmed
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1.6 Complex Numbers

Focus on complex addition and complex conjugate.

Before you solve

Ideas in this lesson

Review the ideas below. Select one to see worked steps and five practice questions.

01Real and imaginary partsWorked steps · five questions02Adding and subtracting complex numbersWorked steps · five questions03Multiplying complex numbersWorked steps · five questions04Dividing complex numbersWorked steps · five questions05Powers of iWorked steps · five questions06Square roots of negative numbersWorked steps · five questions07Complex solutions of quadratic equationsWorked steps · five questions08Complex conjugatesWorked steps · five questions
Lesson brief and rules

1.6 Complex Numbers

i2=−1i^{2}=-1; add real and imaginary parts separately.

Worked example 11
01 / Identify the real part and imaginary part of 3−5i3-5i.
02 / The standard form is a+bia+bi.
03 / Here the real term is 33.
04 / The coefficient multiplying ii is −5-5, not −5i- 5 i.
Worked example 2 · Real and imaginary parts

After simplifying (2+4i)+(−2+2i)(2 + 4 i)+(-2 + 2 i), how should the result be classified?

Combine real parts: 2−2=02-2=0.
Combine imaginary terms to get 6i6 i.
The real part is zero and the imaginary coefficient is nonzero.
Therefore the number is purely imaginary, not real.

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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