Question 1

Which of the following is the correct result of adding the complex numbers $$ (5 + 2i) + (3 - 3i) $$?

Accepted Answer

$$ 8 - i $$

Question 2

Subtract the complex numbers $$ (2 + 6i) - (12 - i) $$ and express your answer in standard form.

Accepted Answer

$$ -10 + 7i $$

Question 3

Multiply the complex numbers $$ (5 + 4i)(6 - 7i) $$ and express your answer in standard form.

Accepted Answer

$$ 62 - 7i $$

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

$$ 11i $$

Question 6

Which of the following is the correct simplification of $$ \sqrt{-80} $$?

Accepted Answer

$$ 4\sqrt{5}i $$

Question 7

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

Accepted Answer

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

Question 8

Simplify $$ i$$^{65}$$ .$$

Accepted Answer

$$ i $$

Question 9

A medical imaging device uses the complex number $$ 7(2 - 9i)  to $$represent a signal. What is the result in standard form?

Accepted Answer

$$ 14 - 63i $$

Question 10

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

Accepted Answer

$$ -2 + 5i $$

Question 11

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

Accepted Answer

$$ 7i $$

Question 12

A circuit designer needs to compute $$ (3 + 2i) - (5 - 7i) . $$What is the result in standard form?

Accepted Answer

$$ -2 + 9i $$

Question 13

Simplify $$ i$$^{31}$$ .$$

Accepted Answer

$$ -i $$

Question 14

Which of the following is the correct result of $$ \sqrt{-64} - \sqrt{-25} $$?

Accepted Answer

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

Question 15

Simplify $$ i$$^{72}$$ .$$

Accepted Answer

$$ 1 $$

Question 16

A chemist is working with the expression $$ \sqrt{-108} . $$What is the simplified form?

Accepted Answer

$$ 6\sqrt{3}i $$

Question 17

Simplify $$ i$$^{114}$$ .$$

Accepted Answer

$$ -1 $$

Question 18

Divide $$ \displaystyle \frac{2 + 3i}{2 - i} $$ and express the result in standard form.

Accepted Answer

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

Question 19

Which of the following is the correct result of $$ \sqrt{-8} + \sqrt{-32} - \sqrt{-24} $$?

Accepted Answer

$$ (2\sqrt{2}i + 4\sqrt{2}i - 2\sqrt{6}i) = 6\sqrt{2}i - 2\sqrt{6}i $$

Question 20

A physicist needs to multiply $$ 3(7 - 5i) . $$What is the result in standard form?

Accepted Answer

$$ 21 - 15i $$

Step-by-Step Guidance for Complex Numbers in Precalculus

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