Free Printable WorksheetMathAlgebra IIMath CurriculumN-CN.7

ALG2.25 Using Complex Numbers to Solve Quadratics Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.25 Using Complex Numbers to Solve Quadratics. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.25 Using Complex Numbers to Solve Quadratics - Select the correct solution(s) to quadratic equations with negative discriminants and express solutions in a + bi form. Associated source-listed standards: CCSS N-CN.7; A-REI.4b; CA CCSSM N-CN.7; A-REI.4b; MA 2017 N-CN.7; A-REI.4b; NY NGLS N-CN.7; A-REI.4b; TX TEKS Algebra II: §111.40.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.25 Using Complex Numbers to Solve Quadratics skill assessments:

Problem 1Difficulty: Mastery

Which quadratic equation with the least positive leading coefficient has solutions -1 + 2i and -1 - 2i?

Ax² + 2x - 5 = 0

Bx² + 2x + 5 = 0

Cx² + 5x + 2 = 0

Dx² - 2x + 5 = 0

Solution & Explanation:The sum of the roots is -2 and the product is 5. Using x² - (sum)x + product = 0 gives x² + 2x + 5 = 0.

Problem 2Difficulty: Mastery

For 2x² + 12x + 25 = 0, what are the real and imaginary parts of each solution?

AThe real part is -3/2, and the imaginary part is ±sqrt(14).

BThe real part is -3, and the imaginary part is ±sqrt(14).

CThe real part is 3, and the imaginary part is ±sqrt(14)/2.

DThe real part is -3, and the imaginary part is ±sqrt(14)/2.

Solution & Explanation:Using the quadratic formula, x = (-12 ± sqrt(-56))/4 = (-12 ± i*2*sqrt(14))/4 = -3 ± (sqrt(14)/2)i. So each solution has real part -3 and imaginary part ±sqrt(14)/2.

Problem 3Difficulty: Mastery

Which step is correct when solving x² + 6x + 25 = 0 by completing the square?

AAdd 25 to both sides to get (x + 6)² = 25.

BSquare the binomial immediately to get (x + 6)² = -25.

CMove 25 first, then add 9: x² + 6x = -25 becomes (x + 3)² = -16.

DMove 25 first, then add 9: x² + 6x = -25 becomes (x + 3)² = 16.

Solution & Explanation:To complete the square, start with x² + 6x = -25. Add (6/2)² = 9 to both sides, giving (x + 3)² = -16, which then leads to x = -3 ± 4i.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard N-CN.7 (Select the correct solution(s) to quadratic equations with negative discriminants and express solutions in a + bi form. Associated source-listed standards: CCSS N-CN.7; A-REI.4b; CA CCSSM N-CN.7; A-REI.4b; MA 2017 N-CN.7; A-REI.4b; NY NGLS N-CN.7; A-REI.4b; TX TEKS Algebra II: §111.40.).