Q: Which of the following best describes an imaginary number?

A complex number of the form $$a + bi$$ where $$b \neq 0$$

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 standard form of the complex number resulting from $$\sqrt{-16}$$?

Accepted Answer

$$4i$$

Question 3

Simplify the expression $$(3 + 5i) + (-2 + 3i)$$ and write your answer in standard form.

Accepted Answer

$$1 + 8i$$

Question 4

Which of the following is the conjugate of the complex number $$7 - 4i$$?

Accepted Answer

$$7 + 4i$$

Question 5

If $$z = 2 + 5i$$ and $$w = 2 - 5i$$, what is $$z \cdot w$$?

Accepted Answer

$$29$$

Question 6

Which of the following best describes an imaginary number?

Accepted Answer

A complex number of the form $$a + bi$$ where $$b 
eq 0$$

Question 7

Simplify $$(6 + 4i) - (3 + 6i)$$ and write your answer in standard form.

Accepted Answer

$$3 - 2i$$

Question 8

Multiply $$(5 + 3i)(2 + 7i)$$ and write your answer in standard form.

Accepted Answer

$$-11 + 41i$$

Question 9

What is $$(4 + 3i)^2$ in standard form?

Accepted Answer

$$7 + 24i$$

Question 10

Divide $$\dfrac{1 + 4i}{5 - 12i}$$ and write your answer in standard form.

Accepted Answer

$$-\dfrac{43}{169} + \dfrac{32}{169}i$$

Question 11

A medical imaging device uses the complex number $$a + bi to $$represent electrical signals. If the real part is $$-3$$ and the imaginary part is $$4$$, what is the modulus (magnitude) of the signal?

Accepted Answer

$$5$$

Question 12

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

Accepted Answer

$$5i$$

Question 13

A chemical reaction is modeled by the complex number $$z = 2 - 3i. $$What is the result of $$\overline{z}$$, the conjugate of $$z$$?

Accepted Answer

$$2 + 3i$$

Question 14

Divide $$\dfrac{2 - 3i}{4 - 3i}$$ and write your answer in standard form.

Accepted Answer

$$\dfrac{5}{25} - \dfrac{6}{25}i$$

Question 15

Which of the following statements is TRUE about the multiplication of complex numbers $$(a + bi)(a - bi)$$?

Accepted Answer

The result is always a real number: $$a^2$$ + $$b^2$$

Question 16

If $$i^2 = -1$, what is i^4$?

Accepted Answer

$$1$$

Question 17

A signal in an electrical circuit is represented by the complex number $$-6 + 8i. $$What is the real part of this number?

Accepted Answer

$$-6$$

Question 18

Which of the following is NOT a complex number in standard form?

Accepted Answer

$$\sqrt{-9}$$

Question 19

If $$a = 0$$ and $$b 
eq 0$$, what type of number is $$a + bi$$?

Accepted Answer

A pure imaginary number

Question 20

A physicist is analyzing a wave represented by $$z = 7 + 24i. $$What is the modulus (magnitude) of $$z$$?

Accepted Answer

$$25$$

Complex Numbers: Definitions, Operations, and Examples

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