Precalculus Polar Form and De Moivre’s Theorem Quiz: 10 Questions with Explanations

Precalculus math quiz: Polar Form and De Moivre's Theorem – Maths PDF

Cover of the book Precalculus Math Tests with Answer Keys (PDF)

Download as a PDFThe Precalculus tests book with answer keysPrintable PDFSee the book ›

Sommaire

This polar complex quiz for Precalculus covers polar form and de moivre's theorem (Common Core N-CN.B.4, N-CN.B.5, N-CN.B.6), with a free PDF to print.

Pick the best answer for 10 questions on polar form, powers and roots of complex numbers. Explanations point out typical errors, such as adding moduli.

Precalculus · Common Core State Standards: N-CN.B.4, N-CN.B.5, N-CN.B.6

Polar complex quiz: 10 questions

Question 1

What is the modulus of \(3-4i\)?

Question 2

Which is the polar form of \(i\)?

Question 3

Multiply \(2\,\text{cis}\,20^{\circ}\) and \(5\,\text{cis}\,70^{\circ}\). The figure shows a similar product.

Product of two complex numbers.

Question 4

The figure shows \(z=1+\sqrt3\,i\). What is its argument?

Complex number z.

Question 5

Evaluate \(\left(\text{cis}\,30^{\circ}\right)^{6}\).

Question 6

What is \((1+i)^{2}\) in polar form?

Question 7

How many distinct fifth roots does \(32\) have?

Question 8

The cube roots of 8 are plotted. What shape do they form?

Three roots.

Question 9

Divide \(8\,\text{cis}\,150^{\circ}\) by \(2\,\text{cis}\,30^{\circ}\).

Question 10

Multiplying a complex number by \(\text{cis}\,90^{\circ}\) does what?

Remember

z = a + bi = r(cos theta + i sin theta) with r = sqrt(a^2 + b^2) and tan theta = b/a.
Product: multiply moduli, add arguments. Quotient: divide moduli, subtract arguments.
De Moivre: [r cis theta]^n = r^n cis(n theta).
nth roots: (r)^(1/n) cis((theta + 360 k)/n), k = 0, …, n – 1.
The n roots form a regular n-gon on a circle of radius r^(1/n).

How to use this polar complex quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the polar complex quiz as a PDF with the button below and keep it with your notes.

All Precalculus chapters: Precalculus math.

Voter.. post

Free printable PDF