Multiplying and squaring complex numbers (ACT). Game on.

Multiplying and squaring complex numbers (ACT) is a grade 11 math skill aligned to Common Core standard HSN.CN.A.2: use the relation i² = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 multiplying and squaring complex numbers (act) problems our math games drill.

CCSS HSN.CN.A.210 questions in the bank
Kickoff

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Warm-upmedium

(−1+5i)(2−3i)=(-1+5i)(2-3i)=

Expand: (−1+5i)(2−3i)=−2+3i+10i−15i2(-1+5i)(2-3i)=-2+3i+10i-15i^{2}. Since i2=−1i^{2}=-1, this is −2+13i+15=13+13i.-2+13i+15=13+13i\textsf{.}

Mid-gamemedium

What is the value of (4+i)(3+2i)(4+i)(3+2i)?

Expand: (4+i)(3+2i)=12+8i+3i+2i2(4+i)(3+2i)=12+8i+3i+2i^{2}. Since i2=−1i^{2}=-1, this is 12+11i−2=10+11i.12+11i-2=10+11i\textsf{.}

Mid-gamemedium

(1+6i)(1−6i)(1+6i)(1-6i) is equal to which of the following?

Expand: (1+6i)(1−6i)=1−6i+6i−36i2=1−36i2(1+6i)(1-6i)=1-6i+6i-36i^{2}=1-36i^{2}. Since i2=−1i^{2}=-1, this is 1+36=37.1+36=37\textsf{.}

Mid-gamemedium

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

Expand: (3+2i)2=9+12i+4i2(3+2i)^{2}=9+12i+4i^{2}. Since i2=−1i^{2}=-1, this is 9+12i−4=5+12i.9+12i-4=5+12i\textsf{.}

Mid-gamemedium

Simplify (4−i)2(4-i)^{2}.

Expand: (4−i)2=16−8i+i2(4-i)^{2}=16-8i+i^{2}. Since i2=−1i^{2}=-1, this is 16−8i−1=15−8i.16-8i-1=15-8i\textsf{.}

Mid-gamehard

Multiply: (5−3i)(−2+i)(5-3i)(-2+i).

Expand: (5−3i)(−2+i)=−10+5i+6i−3i2(5-3i)(-2+i)=-10+5i+6i-3i^{2}. Since i2=−1i^{2}=-1, this is −10+11i+3=−7+11i.-10+11i+3=-7+11i\textsf{.}

Mid-gamehard

(2+5i)2=(2+5i)^{2}=

Expand: (2+5i)2=4+20i+25i2(2+5i)^{2}=4+20i+25i^{2}. Since i2=−1i^{2}=-1, this is 4+20i−25=−21+20i.4+20i-25=-21+20i\textsf{.}

Buzzer beaterhard

Which of the following is equal to (−3+4i)2(-3+4i)^{2}?

Expand: (−3+4i)2=9−24i+16i2(-3+4i)^{2}=9-24i+16i^{2}. Since i2=−1i^{2}=-1, this is 9−24i−16=−7−24i.9-24i-16=-7-24i\textsf{.}

Overtime

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Tests that cover multiplying and squaring complex numbers (act):
ACTPARCCNY State MathMCAP
Reporting domains for this skill
ACT All grades: Preparing for Higher MathATLAS Algebra I: Number and QuantityATLAS Algebra II: Number and QuantityDC CAPE Algebra II: Complex Numbers and Quadratic EquationsGeorgia Milestones Algebra II: The Complex Number SystemISASP High School: Number and Quantity
More Grade 11 skills
Binomial theorem and factorialsComplex number operationsArithmetic sequence nth termRewriting complex numbersAbsolute value equation solutionsConic sectionsExponential and log formulasFinding inverse functions (ACT)All Grade 11 practice →

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