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TRIG.137 Apply De Moivre's theorem to compute powers 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.137 Apply De Moivre's theorem to compute powers of complex numbers. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.137 Apply De Moivre's theorem to compute powers of complex numbers - Apply De Moivres theorem to compute powers of complex numbers

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.137 Apply De Moivre's theorem to compute powers of complex numbers skill assessments:

Problem 1Difficulty: Mastery

Let z = 4 (cos 205 degrees + i sin 205 degrees). Let z = 4 (cos 205 degrees + i sin 205 degrees). Which option is z to the 13th power, written in trig (polar) form?

A67108864 (cos 350 degrees + i sin 350 degrees)

B67108864 (cos 300 degrees + i sin 300 degrees)

C67108864 (cos 215 degrees + i sin 215 degrees)

D67108864 (cos 145 degrees + i sin 145 degrees)

Solution & Explanation:By De Moivre, z to the power of n = r to the power of n(cos(n*theta) + i sin(n*theta)). Here r to the power of n = 67108864 and n*theta = 2665 degrees, which reduces to 145 degrees. So the correct option is 67108864 (cos 145 degrees + i sin 145 degrees).

Problem 2Difficulty: Mastery

Let z = 2 (cos 12 degrees + i sin 12 degrees). Let z = 2 (cos 12 degrees + i sin 12 degrees). Which option is z to the 50th power, written in trig (polar) form?

A1125899906842624 (cos 252 degrees + i sin 252 degrees)

B1125899906842624 (cos 228 degrees + i sin 228 degrees)

C1125899906842624 (cos 240 degrees + i sin 240 degrees)

D1125899906842624 (cos 120 degrees + i sin 120 degrees)

Solution & Explanation:By De Moivre, z to the power of n = r to the power of n(cos(n*theta) + i sin(n*theta)). Here r to the power of n = 1125899906842624 and n*theta = 600 degrees, which reduces to 240 degrees. So the correct option is 1125899906842624 (cos 240 degrees + i sin 240 degrees).

Problem 3Difficulty: Mastery

A unit complex number is given. Let z = cos 135 degrees + i sin 135 degrees. Compute z to the 64th power. Give the result in a + bi form.

Solution & Explanation:With r = 1, z to the power of 64 = cos(64*135) + i sin(64*135). Reduce 8640 degrees to 0 degrees (since 8640 = 24*360), so the value is 1.

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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.137 (Apply De Moivres theorem to compute powers of complex numbers).