Question 1

Which of the following is the correct definition of the imaginary unit $$i$$?

Accepted Answer

$$i = \sqrt{-1}$$

Question 2

What is the sum of $$(5 - 2i) + (3 + 3i)$$?

Accepted Answer

$$8 + i$$

Question 3

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

Accepted Answer

Question 4

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

Accepted Answer

$$14 - 63i$$

Question 5

Divide $$\frac{3}{4i}$$ and express the result in standard form.

Accepted Answer

$$-\frac{3}{4}i$$

Question 6

Simplify $$\sqrt{-121}$$ and write the result in standard form.

Accepted Answer

$$11i$$

Question 7

Simplify $$\sqrt{-80}$$ and write the result in standard form.

Accepted Answer

$$4\sqrt{5}i$$

Question 8

What is $$i^{65}$$?

Accepted Answer

$$i$$

Question 9

A medical imaging device uses the complex number $$7 + 5i to $$represent a signal. If the device multiplies this signal by $$3$$, what is the new signal in standard form?

Accepted Answer

$$21 + 15i$$

Question 10

Simplify $$\sqrt{-49}$$ and write the result in standard form.

Accepted Answer

$$7i$$

Question 11

A chemical reaction produces a result represented by the complex number $$(5 + 4i)(6 - 7i). $$What is the product in standard form?

Accepted Answer

$$62 - 11i$$

Question 12

Divide $$\frac{5}{2 + i}$$ and express the result in standard form.

Accepted Answer

$$2 - i$$

Question 13

Simplify $$i^{72}.$$

Accepted Answer

$$1$$

Question 14

Perform the operation $$\sqrt{-27} + \sqrt{-48}$$ and write the result in standard form.

Accepted Answer

$$3\sqrt{3}i + 4\sqrt{3}i = 7\sqrt{3}i$$

Question 15

Simplify $$i^{31}.$$

Accepted Answer

$$-i$$

Question 16

A signal in an electrical circuit is represented by $$2 - 3i. If $$the signal is divided by $$2 + i$$, what is the result in standard form?

Accepted Answer

$$\frac{1}{5} - \frac{8}{5}i$$

Question 17

Simplify $$\sqrt{-108}$$ and write the result in standard form.

Accepted Answer

$$6\sqrt{3}i$$

Question 18

Simplify $$i^{114}.$$

Accepted Answer

$$-1$$

Question 19

A medical device uses the complex number $$(3 + 2i) - (5 - 7i) to $$represent a change in signal. What is the result in standard form?

Accepted Answer

$$-2 + 9i$$

Question 20

Simplify $$\sqrt{-64} - \sqrt{-25}$$ and write the result in standard form.

Accepted Answer

$$8i - 5i = 3i$$

Step-by-Step Guidance for Complex Numbers in Precalculus

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