Question 1

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + b\,i$$

Question 2

Identify the real and imaginary parts of the complex number $$-4 + 9i.$$

Accepted Answer

Real part: $$-4$$, Imaginary part: $$9$$

Question 3

Express $$\dfrac{9 + \sqrt{16}i}{3} in $$standard form.

Accepted Answer

$$3 + 4i$$

Question 4

What is the result of $$(2 + 8i) - (4 - i) in $$standard form?

Accepted Answer

$$6 + 9i$$

Question 5

Find the sum: $$5(4 + 7i) + 6(3 - 2i).$$

Accepted Answer

$$38 + 17i$$

Question 6

Multiply the complex numbers: $$2i(9 - 4i)(6 + 5i).$$

Accepted Answer

$$38i + 62i^2$

Question 7

What is the conjugate of the complex number $$1 - 2i$$?

Accepted Answer

$$1 + 2i$$

Question 8

Multiplying a complex number by its conjugate always results in:

Accepted Answer

A real number

Question 9

Find the product of $$-7 - i$$ and its conjugate.

Accepted Answer

$$50$$

Question 10

Divide $$6 + 4i by$$ $$4 - 2i$$ and express your answer in standard form.

Accepted Answer

$$1.2 + 1.6i$$

Question 11

Which of the following steps is necessary when dividing by a complex number?

Accepted Answer

Multiply numerator and denominator by the conjugate of the denominator

Question 12

If $$a + b i is a $$complex number, what is its conjugate?

Accepted Answer

$$a - b i$$

Question 13

What is the result of $$(3 + 8i) 	imes (3 - 8i)$$?

Accepted Answer

$$73$$

Question 14

A medical imaging device uses the complex number $$5 + 3i to $$represent a signal. What is the magnitude of this signal?

Accepted Answer

$$\sqrt{25 + 9}$$

Question 15

Which operation will always result in a real number when performed on any complex number $$a + b i$$?

Accepted Answer

Multiplying $$a + b i by $$its conjugate

Question 16

A chemist mixes two solutions represented by $$2 + 3i$$ and $$4 - 5i. $$What is the sum in standard form?

Accepted Answer

$$6 - 2i$$

Question 17

Which of the following is the correct result of $$3 + 2\sqrt{3} in $$standard complex form?

Accepted Answer

$$3 + 2\sqrt{3}i$$

Question 18

If $$a + b i$$ and $$a - b i$$ are complex conjugates, what is their product?

Accepted Answer

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

Question 19

A signal in an electrical circuit is represented by $$4 - 5i. $$What is the conjugate of this signal?

Accepted Answer

$$4 + 5i$$

Question 20

Divide $$-5 + 3i by$$ $$-7 - 4i$$ and express your answer in standard form.

Accepted Answer

$$-0.7 + 0.48i$$

Complex Numbers: Definitions, Operations, and Applications

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