Question 1

Which of the following is the standard form of a complex number?

Accepted Answer

$a + b\,i$

Question 2

Identify the real and imaginary parts of the complex number $-4 + 9i$.

Accepted Answer

Real part: $-4$, Imaginary part: $9$

Question 3

Express $\dfrac{9 + \sqrt{16}i}{3}$ in standard form.

Accepted Answer

$3 + 4i$

Question 4

What is the result of $(2 + 8i) - (4 - i)$ in standard form?

Accepted Answer

$6 + 9i$

Question 5

Find the sum: $5(4 + 7i) + 6(3 - 2i)$.

Accepted Answer

$38 + 17i$

Question 6

Multiply the complex numbers: $2i(9 - 4i)(6 + 5i)$.

Accepted Answer

$38i + 62i^2$

Question 7

What is the conjugate of the complex number $1 - 2i$?

Accepted Answer

$1 + 2i$

Question 8

Multiplying a complex number by its conjugate always results in:

Accepted Answer

A real number

Question 9

Find the product of $-7 - i$ and its conjugate.

Accepted Answer

$50$

Question 10

Divide $6 + 4i$ by $4 - 2i$ and express your answer in standard form.

Accepted Answer

$1.2 + 1.6i$

Question 11

Which of the following steps is necessary when dividing by a complex number?

Accepted Answer

Multiply numerator and denominator by the conjugate of the denominator

Question 12

If $a + b i$ is a complex number, what is its conjugate?

Accepted Answer

$a - b i$

Question 13

What is the result of $(3 + 8i) 	imes (3 - 8i)$?

Accepted Answer

$73$

Question 14

A medical imaging device uses the complex number $5 + 3i$ to represent a signal. What is the magnitude of this signal?

Accepted Answer

$\sqrt{25 + 9}$

Question 15

Which operation will always result in a real number when performed on any complex number $a + b i$?

Accepted Answer

Multiplying $a + b i$ by its conjugate

Question 16

A chemist mixes two solutions represented by $2 + 3i$ and $4 - 5i$. What is the sum in standard form?

Accepted Answer

$6 - 2i$

Question 17

Which of the following is the correct result of $3 + 2\sqrt{3}$ in standard complex form?

Accepted Answer

$3 + 2\sqrt{3}i$

Question 18

If $a + b i$ and $a - b i$ are complex conjugates, what is their product?

Accepted Answer

$a^2 + b^2$

Question 19

A signal in an electrical circuit is represented by $4 - 5i$. What is the conjugate of this signal?

Accepted Answer

$4 + 5i$

Question 20

Divide $-5 + 3i$ by $-7 - 4i$ and express your answer in standard form.

Accepted Answer

$-0.7 + 0.48i$

Complex Numbers: Definitions, Operations, and Applications

Study Guide - Practice Questions