Question 1

Which of the following is the correct value of $i^{23}$?

Accepted Answer

$i$

Question 2

A medical imaging device uses the complex number $z = 3 - 4i$ to represent a signal. What is the modulus (magnitude) of this signal?

Accepted Answer

$5$

Question 3

Simplify the expression $\sqrt{-50}$ and express your answer in terms of $i$.

Accepted Answer

$5i\sqrt{2}$

Question 4

A chemical reaction is modeled by the complex number $z = 2 + 5i$. What is the complex conjugate of $z$?

Accepted Answer

$2 - 5i$

Question 5

Which of the following is the result of $(3 + 2i) + (4 - 5i)$?

Accepted Answer

$7 - 3i$

Question 6

A circuit analysis problem gives the product $(2 + 3i)(2 - 3i)$. What is the result?

Accepted Answer

$13$

Question 7

Simplify the quotient $\frac{4 + i}{1 - 2i}$ and express your answer in the form $a + bi$.

Accepted Answer

$-0.2 + 2.2i$

Question 8

Which of the following statements about complex numbers is TRUE?

Accepted Answer

The product of a complex number and its conjugate is always a non-negative real number.

Question 9

A signal in an engineering system is represented by $z = 6 - 8i$. What is $z \cdot \overline{z}$?

Accepted Answer

$100$

Question 10

Simplify $i^{35}$.

Accepted Answer

$-i$

Question 11

A quadratic equation in physics yields the solution $x = \frac{-6 + \sqrt{-16}}{2}$. What is the value of $x$?

Accepted Answer

$-3 + 2i$

Question 12

Which of the following is the standard form of the product $(1 + 2i)(3 - 4i)$?

Accepted Answer

$11 + 2i$

Question 13

Simplify $\sqrt{-27}$.

Accepted Answer

$3i\sqrt{3}$

Question 14

A medical device uses the number $z = 5 + 12i$. What is the argument (angle in radians) of $z$?

Accepted Answer

$\arctan\left(\frac{12}{5}\right)$

Question 15

Which of the following is the result of subtracting $(2 - 3i)$ from $(7 + 4i)$?

Accepted Answer

$5 + 7i$

Question 16

Simplify $\frac{3}{2i}$ and write your answer in standard form $a + bi$.

Accepted Answer

$-\frac{3}{2}i$

Question 17

If $z = 4 + 3i$ and $w = 1 - 2i$, what is $z \cdot w$?

Accepted Answer

$10 - 5i$

Question 18

A quadratic equation in engineering yields the solution $x = \frac{-2 \pm \sqrt{-20}}{4}$. What are the solutions?

Accepted Answer

$-0.5 \pm i\sqrt{1.25}$

Question 19

Which of the following is the correct simplification of $i^{2024}$?

Accepted Answer

$1$

Complex Numbers in College Algebra: Definitions, Operations, and Applications

Study Guide - Practice Questions