$$z = r \cos \theta + r \sin \theta i$$

Question 1

Convert the complex number $$z = 3 \operatorname{cis} 60^\circ to $$rectangular form.

Accepted Answer

$$z = 1.5 + 2.6i$$

Question 2

Convert the complex number $$z = 5 \operatorname{cis} \left( \frac{\pi}{3} \right) to $$rectangular form.

Accepted Answer

$$z = 2.5 + 4.33i$$

Question 3

Which of the following is the correct rectangular form for $$z = 4 \operatorname{cis} 120^\circ$$?

Accepted Answer

$$z = -2 + 3.46i$$

Question 4

Given $$z = 7 \operatorname{cis} 210^\circ$$, what is its rectangular form?

Accepted Answer

$$z = -6.06 - 3.5i$$

Question 5

If $$z = 2 \operatorname{cis} 0^\circ$$, what is the rectangular form of $$z$$?

Accepted Answer

$$z = 2 + 0i$$

Question 6

A phasor in electrical engineering is represented as $$V = 10 \operatorname{cis} 45^\circ. $$What is its rectangular form?

Accepted Answer

$$V = 7.07 + 7.07i$$

Question 7

Convert $$z = 8 \operatorname{cis} 270^\circ to $$rectangular form.

Accepted Answer

$$z = 0 - 8i$$

Question 8

Which of the following is the rectangular form of $$z = 6 \operatorname{cis} 180^\circ$$?

Accepted Answer

$$z = -6 + 0i$$

Question 9

A signal is represented as $$S = 12 \operatorname{cis} 150^\circ. $$What is its rectangular form?

Accepted Answer

$$S = -10.39 + 6i$$

Question 10

Convert $$z = 5 \operatorname{cis} 90^\circ to $$rectangular form.

Accepted Answer

$$z = 0 + 5i$$

Question 11

If $$z = r \operatorname{cis} 	heta$$, which formula correctly converts $$z to $$rectangular form?

Accepted Answer

$$z = r \cos 	heta + r \sin 	heta i$$

Question 12

A rotating object has a position given by $$z = 4 \operatorname{cis} 315^\circ. $$What is its rectangular form?

Accepted Answer

$$z = 2.83 - 2.83i$$

Question 13

Convert $$z = 9 \operatorname{cis} 240^\circ to $$rectangular form.

Accepted Answer

$$z = -4.5 - 7.79i$$

Question 14

Which of the following is the rectangular form of $$z = 2 \operatorname{cis} 135^\circ$$?

Accepted Answer

$$z = -1.41 + 1.41i$$

Question 15

A current in an AC circuit is given by $$I = 3 \operatorname{cis} 270^\circ. $$What is its rectangular form?

Accepted Answer

$$I = 0 - 3i$$

Complex Numbers: Polar and Rectangular Forms

Study Guide - Practice Questions