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 $$i^4$$?

Accepted Answer

$$1$$

Question 3

Which of the following statements is TRUE about complex numbers $$a + bi$$ and $$c + di$$?

Accepted Answer

They are equal if $$a = c$$ and $$b = d$$

Question 4

Simplify $$\sqrt{-36}$$ using $$i.$$

Accepted Answer

$$6i$$

Question 5

Which of the following is a pure imaginary number?

Accepted Answer

$$0 + 5i$$

Question 6

What is the product of $$(3 + 2i)(3 - 2i)$$?

Accepted Answer

$$13$$

Question 7

Simplify $$i^{15}.$$

Accepted Answer

$$i$$

Question 8

Add the complex numbers $$(4 + 3i)$$ and $$(2 - 5i).$$

Accepted Answer

$$6 - 2i$$

Question 9

Divide $$\frac{5 + 2i}{1 - i}$$ and write the answer in standard form.

Accepted Answer

$$\frac{3 + 7i}{2}$$

Question 10

Which of the following is NOT a valid property when simplifying $$\sqrt{ab}$$ for negative $$a$$ and $$b$$?

Accepted Answer

$$\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$$

Question 11

If $$z = 7 + 2i$$, what is the complex conjugate of $$z$$?

Accepted Answer

$$7 - 2i$$

Question 12

Which of the following best describes the set of real numbers in relation to complex numbers?

Accepted Answer

The set of real numbers is a subset of the set of complex numbers.

Question 13

Simplify $$(2 + 5i) + (3 - 7i).$$

Accepted Answer

$$5 - 2i$$

Question 14

Multiply $$(1 + 2i)(2 - 3i)$$ and write the answer in standard form.

Accepted Answer

$$8 + i$$

Question 15

A medical imaging device uses the number $$i in $$its calculations. If the device computes $$i^{2023}$$, what is the result?

Accepted Answer

$$-i$$

Question 16

Which of the following is a nonreal complex number?

Accepted Answer

$$3 + 4i$$

Question 17

Simplify $$\frac{6 + 8i}{2}$$ and write the answer in standard form.

Accepted Answer

$$3 + 4i$$

Question 18

If $$i^2 = -1$, what is i^6$?

Accepted Answer

$$-1$$

Question 19

A chemical reaction produces a result of $$\sqrt{-49}. $$What is the simplified form using $$i$$?

Accepted Answer

$$7i$$

Question 20

Which of the following is the correct result of dividing $$4i by$$ $$2i$$?

Accepted Answer

$$2$$

Complex Numbers: Concepts and Operations (College Algebra Study Notes)

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