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 operationsFactorials (ACT)Arithmetic sequence nth termCalculating permutations (ACT)Rewriting complex numbersAbsolute value equation solutionsCalculating combinations (ACT)All Grade 11 practice →

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