Complex Numbers Practice & Key

Master complex numbers with this Algebra 2 worksheet! Covers operations, conjugates, division, modulus, powers of i, quadratic equations with complex roots, & key.

This comprehensive 5-page worksheet is designed to help Algebra 2 students master complex numbers. It guides learners step-by-step from core definitions of the imaginary unit to complex arithmetic, conjugates, division, powers of i, and solving quadratic equations with complex solutions.

What is Included:

Section A: Concept Check. Evaluates foundational understanding of the imaginary unit i, standard form a + bi, complex conjugates, square roots of negative numbers, and explaining why multiplying a complex number by its conjugate always produces a real number.

Section B: Operations with Complex Numbers. Focuses on performing addition, subtraction, and multiplication with complex numbers, including expanding squared binomial expressions into standard form.

Section C: Conjugates, Division, and Modulus. Covers dividing complex numbers by rationalizing denominators using complex conjugates, finding conjugates, and calculating the modulus of complex numbers.

Section D: Powers of i and Radicals. Guides students through simplifying high powers of i using cyclic patterns, simplifying radicals with negative radicands, and carefully multiplying square roots of negative numbers.

Section E: Complex Solutions to Quadratics. Challenges students to solve quadratic equations yielding complex roots, evaluate discriminants, and verify that complex solutions for quadratics with real coefficients always appear as conjugate pairs.

Teacher Benefits:

Ready to Print & Go – Zero prep required. Excellent for structured lessons, homework, independent practice, or exam review.

Complete Solutions Included – Comes with a fully worked answer key detailing conceptual checks, standard form operations, step-by-step conjugate division, power reductions, and full quadratic formula steps for complex roots.