Question 1

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

Accepted Answer

$$a + bi$$

Question 2

What is the value of $$i^2$$ where $$i is $$the imaginary unit?

Accepted Answer

$$-1$$

Question 3

Add the complex numbers $$3 + 4i$$ and $$2 - 5i. $$What is the result in standard form?

Accepted Answer

$$5 - i$$

Question 4

Subtract $$7 - 2i$$ from $$4 + 6i. $$What is the result in standard form?

Accepted Answer

$$-3 + 8i$$

Question 5

Multiply the complex numbers $$2 + 3i$$ and $$1 - 4i. $$What is the result in standard form?

Accepted Answer

$$14 - 5i$$

Question 6

What is the conjugate of the complex number $$5 - 7i$$?

Accepted Answer

$$5 + 7i$$

Question 7

Divide $$6 + 8i by$$ $$2 - 3i$$ and express the result in standard form.

Accepted Answer

$$-1.38 + 3.69i$$

Question 8

Which of the following is the principal square root of $$-25$$?

Accepted Answer

$$5i$$

Question 9

A medical device uses the formula $$z = 4 + 3i to $$represent an electrical signal. What is the conjugate of this signal?

Accepted Answer

$$4 - 3i$$

Question 10

If $$z = 2 + 5i$$ and $$w = 2 - 5i$$, what is $$z 	imes w$$?

Accepted Answer

$$29$$

Question 11

Which of the following best describes the set of all numbers of the form $$a + bi$$ where $$a$$ and $$b$$ are real numbers?

Accepted Answer

Complex numbers

Question 12

A chemical reaction produces a result of $$\sqrt{-36}. $$What is the principal square root in standard form?

Accepted Answer

$$6i$$

Question 13

Which operation is used to simplify the denominator when dividing complex numbers?

Accepted Answer

Multiplying by the conjugate of the denominator

Question 14

If $$z = 3 + 4i$$, what is $$|z|$$, the modulus of $$z$$?

Accepted Answer

$$5$$

Question 15

Which of the following is NOT a complex number?

Accepted Answer

None of the above

Complex Numbers: Operations and Properties

Study Guide - Practice Questions