Complex number operations. Game on.

Complex number operations is a grade 11 math skill aligned to Common Core standard HSN.CN.A.1 and HSN.CN.A.2: know there is a complex number i such that i² = −1, and every complex number has the form a + bi with a and b real. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 17 complex number operations problems our math games drill.

CCSS HSN.CN.A.1 CCSS HSN.CN.A.217 questions in the bank

Kickoff

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Warm-upeasy

What is $|6 + 8i|$ ?

$|6 + 8i| = \sqrt{6^2 + 8^2} = \sqrt{100} = 10$ .

Mid-gameeasy

What is $(3i)^{2}$ ?

$(3i)^{2} = 9i^{2} = 9(-1) = -9$ .

Mid-gameeasy

What is $i^{3}$ ?

$i^{3} = i^{2} \cdot i = (-1)(i) = -i$ .

Mid-gameeasy

What is $|5 + 12i|$ ?

$|5 + 12i| = \sqrt{5^2 + 12^2} = \sqrt{169} = 13$ .

Mid-gameeasy

What is $(2i)^2$ ?

$(2i)^2 = 4i^2 = 4(-1) = -4$ .

Mid-gameeasy

What is $i^{6}$ ?

$i^{6} = (i^{2})^{3} = (-1)^{3} = -1$ .

Mid-gameeasy

What is $|8 + 15i|$ ?

$|8 + 15i| = \sqrt{8^2 + 15^2} = \sqrt{289} = 17$ .

Buzzer beatereasy

What is $(4i)^2$ ?

$(4i)^2 = 16i^2 = 16(-1) = -16$ .

Overtime

9 more. Played, not assigned.

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Tests that cover complex number operations:

ACT PARCC NY State Math MCAP

Reporting domains for this skill

ACT All grades: Preparing for Higher Math ATLAS Algebra I: Number and Quantity ATLAS Algebra II: Number and Quantity DC CAPE Algebra II: Complex Numbers and Quadratic Equations Georgia Milestones Algebra II: The Complex Number System ISASP High School: Number and Quantity

More Grade 11 skills

Multiplying and squaring complex numbers (ACT)Rewriting complex numbers Binomial theorem and factorials Exponential and log formulas Arithmetic sequence nth term Finding inverse functions (ACT)Absolute value equation solutions Conic sections All Grade 11 practice →

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