Grade 11 · Algebra & functions

Complex number operations practice

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

Sample questions

Try 8 for free

Question 1easy

What is $|6 + 8i|$ ?

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

Question 2easy

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

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

Question 3easy

What is $i^{3}$ ?

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

Question 4easy

What is $|5 + 12i|$ ?

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

Question 5easy

What is $(2i)^2$ ?

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

Question 6easy

What is $i^{6}$ ?

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

Question 7easy

What is $|8 + 15i|$ ?

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

Question 8easy

What is $(4i)^2$ ?

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

Tests that cover complex number operations:

ACT PARCC NY State Math MCAP

More Grade 11 skills:

Binomial theorem and factorials Conic sections Exponential and log formulas Function transformations Geometric sequence equations Logarithm rules Sequences and series All Grade 11 practice →

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