Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.PPC.4

TRIG.128 De Moivre's theorem and roots of complex numbers Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.128 De Moivre's theorem and roots of complex numbers. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.128 De Moivre's theorem and roots of complex numbers - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.4. Skill statement in this prompt cell: Select the correct result of applying De Moivre's theorem to compute a power or roots and identify the geometric pattern of roots on the complex plane. Associated standards listed with this skill in this prompt cell: UTRI.PPC.4; CCSS HSN.CN.B.5-6 (+). Use this prompt-provided wording as the supporting standard description for this workflow.

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.128 De Moivre's theorem and roots of complex numbers skill assessments:

Problem 1Difficulty: Mastery
Use the complex-plane diagram of the eight roots of z8 = 256 cis(0 degrees), plotted on a circle of radius 2 at 45-degree intervals. If each plotted root is squared, what set of distinct points results?
AThe fourth roots of 256 cis(0 degrees): radius 4 at 0, 90, 180, and 270 degrees
BThe eighth roots of 256 cis(0 degrees): radius 2 at 45-degree intervals
CThe fourth roots of 16 cis(0 degrees): radius 2 at 0, 90, 180, and 270 degrees
DOne point only: 4 cis(0 degrees)
Solution & Explanation:Squaring each root doubles its angle and squares its modulus, giving radius 4. The doubled angles collapse to 0, 90, 180, and 270 degrees, the fourth roots of 256 cis(0 degrees).
Problem 2Difficulty: Mastery
If 7 cis(14 degrees) is one seventh root of W, what is the argument of W in degrees reduced to [0, 360)? Enter only the number.
Solution & Explanation:Raise the root to the seventh power: the original argument is 7(14 degrees) = 98 degrees.
Problem 3Difficulty: Mastery
Simplify (4 cis(11pi/12))2 in rectangular form.
A8sqrt(3) + 8i
B8sqrt(3) - 8i
C-8sqrt(3) + 8i
D-8sqrt(3) - 8i
Solution & Explanation:Squaring gives 16 cis(11pi/6). Since cos(11pi/6) = sqrt(3)/2 and sin(11pi/6) = -1/2, the value is 8sqrt(3) - 8i.

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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 Trigonometry Math students. It aligns with educational standard UTRI.PPC.4 (Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.4. Skill statement in this prompt cell: Select the correct result of applying De Moivre's theorem to compute a power or roots and identify the geometric pattern of roots on the complex plane. Associated standards listed with this skill in this prompt cell: UTRI.PPC.4; CCSS HSN.CN.B.5-6 (+). Use this prompt-provided wording as the supporting standard description for this workflow.).

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