Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.PPC.3

TRIG.127 Complex numbers in polar (trigonometric) form Worksheet

Download our free printable Trigonometry Math worksheet on TRIG.127 Complex numbers in polar (trigonometric) form. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Prefer interactive practice with instant grading and explanations?Practice Complex numbers in polar (trigonometric) form Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.127 Complex numbers in polar (trigonometric) form. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.127 Complex numbers in polar (trigonometric) form - Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.3. Skill statement in this prompt cell: Select the correct polar form of a complex number (modulus and argument) and interpret the argument as a rotation. Associated standards listed with this skill in this prompt cell: UTRI.PPC.3; CCSS HSN.CN.B.4 (+); MA 2017 N-CN (+). 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.127 Complex numbers in polar (trigonometric) form skill assessments:

Problem 1Difficulty: Mastery
A complex number has endpoint in Quadrant III, modulus 2sqrt(13), and reference-angle tangent 2/3. Which polar form matches z = -6 - 4i?
Az = 2sqrt(13)(cos(arctan(2/3)) + i sin(arctan(2/3)))
Bz = 2sqrt(13)(cos(pi - arctan(2/3)) + i sin(pi - arctan(2/3)))
Cz = 2sqrt(13)(cos(pi + arctan(2/3)) + i sin(pi + arctan(2/3)))
Dz = 2sqrt(13)(cos(2pi - arctan(2/3)) + i sin(2pi - arctan(2/3)))
Solution & Explanation:The point -6 - 4i is in Quadrant III. The reference angle has tan(theta) = 4/6 = 2/3, so the standard argument is pi + arctan(2/3).
Problem 2Difficulty: Mastery
The polar expression z = 12(cos(9pi/4) + i sin(9pi/4)) is rewritten with the smallest nonnegative argument. Which form is correct?
Az = 12(cos(pi/4) + i sin(pi/4))
Bz = 12(cos(3pi/4) + i sin(3pi/4))
Cz = 9(cos(pi/4) + i sin(pi/4))
Dz = 12(cos(7pi/4) + i sin(7pi/4))
Solution & Explanation:Subtract 2pi from 9pi/4 to get pi/4. The modulus remains 12.
Problem 3Difficulty: Mastery
A complex number has modulus 6 and is described as a clockwise rotation of pi/4 from the positive real axis. Which standard polar form uses 0 <= theta < 2pi?
Az = 6(cos(pi/4) + i sin(pi/4))
Bz = 6(cos(3pi/4) + i sin(3pi/4))
Cz = 6(cos(5pi/4) + i sin(5pi/4))
Dz = 6(cos(7pi/4) + i sin(7pi/4))
Solution & Explanation:A clockwise rotation of pi/4 is -pi/4. The coterminal angle in [0, 2pi) is 7pi/4.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this TRIG.127 Complex numbers in polar (trigonometric) form worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this TRIG.127 Complex numbers in polar (trigonometric) form worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice TRIG.127 Complex numbers in polar (trigonometric) form online with instant feedback?

Yes! In addition to this printable worksheet, students can practice TRIG.127 Complex numbers in polar (trigonometric) form interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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.3 (Primary standard selected for prompt fields in this prompt cell: UTRI.PPC.3. Skill statement in this prompt cell: Select the correct polar form of a complex number (modulus and argument) and interpret the argument as a rotation. Associated standards listed with this skill in this prompt cell: UTRI.PPC.3; CCSS HSN.CN.B.4 (+); MA 2017 N-CN (+). Use this prompt-provided wording as the supporting standard description for this workflow.).

Related Trigonometry Math Resources

Continue learning with complementary skill worksheets and online practice