Free Printable WorksheetMathTrigonometryMath CurriculumTRIG.136

TRIG.136 Multiply and divide complex numbers using polar form Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.136 Multiply and divide complex numbers using polar form. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.136 Multiply and divide complex numbers using polar form - Multiply and divide complex numbers using polar form

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

Trigonometry

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 TRIG.136 Multiply and divide complex numbers using polar form skill assessments:

Problem 1Difficulty: Mastery

Simplify: (2 exp(i*3pi over 4))(8 cis -5pi over 8) divided by (4 exp(i*7pi over 8)). Give the answer as r cis theta with theta in (-pi, pi].

Solution & Explanation:Modulus: (2*8) divided by 4 = 4. Angle: 3pi over 4 + (-5pi over 8) - 7pi over 8 = 6pi over 8 - 5pi over 8 - 7pi over 8 = -6pi over 8 = -3pi over 4, which is already a principal value.

Problem 2Difficulty: Mastery

Compute and simplify: (5 cis 40 deg)(10 cis 200 deg) divided by (25 cis -130 deg). Give theta in [0,360).

Solution & Explanation:Modulus: (5*10) divided by 25 = 50 divided by 25 = 2. Angle: 40 deg + 200 deg - (-130 deg) = 370 deg. Reduce: 370 deg - 360 deg = 10 deg.

Problem 3Difficulty: Mastery

z has modulus 9 and satisfies (z)(3 cis -2pi over 5) = 27 cis 7pi over 5. Find the principal argument of z.

Solution & Explanation:From the moduli: 9*3 = 27, so that part matches. For angles: arg(z) + (-2pi over 5) = 7pi over 5, so arg(z) = 7pi over 5 + 2pi over 5 = 9pi over 5. Convert to a principal value by subtracting 2pi: 9pi over 5 - 2pi = 9pi over 5 - 10pi over 5 = -pi over 5.

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Frequently Asked Questions

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QIs this TRIG.136 Multiply and divide complex numbers using polar form worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard TRIG.136 (Multiply and divide complex numbers using polar form).