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 $$i^2$$?

Accepted Answer

$$-1$$

Question 3

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

Accepted Answer

$$8 + i$$

Question 4

Subtract $$(12 - i)$$ from $$(2 + 6i). $$What is the result in standard form?

Accepted Answer

$$-10 + 7i$$

Question 5

Multiply $$7i by$$ $$(2 - 9i). $$What is the result in standard form?

Accepted Answer

$$63 + 14i$$

Question 6

Find the product of $$(5 + 4i)$$ and $$(6 - 7i).$$

Accepted Answer

$$58 - 11i$$

Question 7

What is the conjugate of the complex number $$a + bi$$?

Accepted Answer

$$a - bi$$

Question 8

What is the product of a complex number and its conjugate, $$(a + bi)(a - bi)$$?

Accepted Answer

$$a^2$$ + $$b^2$$

Question 9

Divide $$\dfrac{5 + 4i}{4 - i}$$ and express the result in standard form.

Accepted Answer

$$\dfrac{16 + 21i}{17}$$

Question 10

What is the principal square root of $$-27$$?

Accepted Answer

$$3i\sqrt{3}$$

Question 11

Simplify $$\sqrt{-27} + \sqrt{-48}.$$

Accepted Answer

$$7i\sqrt{3}$$

Question 12

Expand $$(-2 - \sqrt{3})^2$ and write the result in standard form.

Accepted Answer

$$1 + 4i\sqrt{3}$$

Question 13

Which of the following best describes the set of all complex numbers?

Accepted Answer

All numbers of the form $$a + bi$$ where $$a$$ and $$b$$ are real numbers

Question 14

A medical imaging device uses the number $$2 + 3i to $$represent a signal. If the conjugate is used in a calculation, what value is used?

Accepted Answer

$$2 - 3i$$

Question 15

If $$i is $$the imaginary unit, which of the following is true for any positive real number $$b$$?

Accepted Answer

$$\sqrt{-b} = i\sqrt{b}$$

Question 16

A physicist is analyzing a wave with amplitude $$4 - 5i. $$What is the product of this amplitude and its conjugate?

Accepted Answer

$$41$$

Complex Numbers: Operations and Properties

Study Guide - Practice Questions