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

A medical imaging device uses alternating current described by the complex number $$ (7 + 2i) + (1 - 4i) . $$What is the sum in standard form?

Accepted Answer

$$8 - 2i$$

Question 3

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

Accepted Answer

$$-10 + 7i$$

Question 4

Multiply $$ 7(2 - 9i) $$ and express the result in standard form.

Accepted Answer

$$14 - 63i$$

Question 5

Multiply $$ (5 + 4i)(6 - 7i) $$ and express the result in standard form.

Accepted Answer

$$62 - 11i$$

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

$$-2 + 5i$$

Question 8

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

Accepted Answer

$$11i$$

Question 9

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

Accepted Answer

$$4i\sqrt{5}$$

Question 10

A physicist is analyzing a wave function and needs to simplify $$ \sqrt{-108} . $$What is the result in standard form?

Accepted Answer

$$6i\sqrt{3}$$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$$i$$

Question 14

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

Accepted Answer

$$1$$

Question 15

A chemist is working with a formula involving $$ i$$^{31}$$ . $$What is the simplified value?

Accepted Answer

$$-i$$

Question 16

Simplify $$ (3 + 2i) - (5 - 7i) $$ and express the result in standard form.

Accepted Answer

$$-2 + 9i$$

Question 17

Multiply $$ (5 - 4i)(3 + i) $$ and express the result in standard form.

Accepted Answer

$$19 - 7i$$

Question 18

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

Accepted Answer

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

Question 19

Simplify $$ \sqrt{-2} \cdot \sqrt{-7} \cdot \sqrt{4} \cdot \sqrt{5} \cdot \sqrt{4} $$ and write the result in standard form.

Accepted Answer

$$80i$$

Question 20

Simplify $$ \sqrt{-23} \cdot \sqrt{4} \cdot \sqrt{2} \cdot \sqrt{5} $$ and write the result in standard form.

Accepted Answer

$$20i\sqrt{46}$$

Step-by-Step Guidance for Complex Numbers in Precalculus

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