Question 1

Which of the following is the correct definition of a complex number?

Accepted Answer

$$a + bi$$, where $$a$$ and $$b$$ are real numbers and $$i = \sqrt{-1}$$

Question 2

What is the value of $$i^2$$?

Accepted Answer

$$-1$$

Question 3

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

Accepted Answer

$$a + bi$$

Question 4

If $$z = 3 - 4i$$, what is the complex conjugate of $$z$$?

Accepted Answer

$$3 + 4i$$

Question 5

Add the complex numbers $$(-2 + 5i)$$ and $$(3 - 4i). $$What is the result in standard form?

Accepted Answer

$$1 + i$$

Question 6

Subtract $$(2 - 3i)$$ from $$(5 + 2i). $$What is the result?

Accepted Answer

$$3 + 5i$$

Question 7

Multiply $$(2 + 3i)$$ and $$(1 - 4i). $$What is the result in standard form?

Accepted Answer

$$14 - 5i$$

Question 8

Divide $$8 - 12i by$$ $$5 + 4i$$ and write the result in standard form.

Accepted Answer

$$\frac{8 - 12i}{5 + 4i} = \frac{8 \cdot 5 + 8 \cdot 4i - 12i \cdot 5 - 12i \cdot 4i}{(5 + 4i)(5 - 4i)} = \frac{76 - 68i}{41} = \frac{76}{41} - \frac{68}{41}i$$

Question 9

Which of the following statements is TRUE about the real and imaginary parts of a complex number $$a + bi$$?

Accepted Answer

$$a is $$the real part and $$b is $$the imaginary part

Question 10

A medical imaging device uses the number $$4 - 3i to $$represent a signal. If the device receives a signal $$2 + 5i at $$the same time, what is the sum of the two signals?

Accepted Answer

$$6 + 2i$$

Question 11

If $$i = \sqrt{-1}$$, what is the value of $$i^4$$?

Accepted Answer

$$1$$

Question 12

Which of the following is NOT a complex number?

Accepted Answer

$$\sqrt{2}$$

Question 13

A chemical reaction is modeled by the equation $$z = 2 + 3i. $$What is the result if the reaction is reversed, represented by the conjugate of $$z$$?

Accepted Answer

$$2 - 3i$$

Question 14

Which operation is performed first when multiplying two complex numbers $$(a + bi)(c + di)$$?

Accepted Answer

Multiply $$a by$$ $$c$$

Question 15

If $$z_1 = 1 + 2i$ and z_2$ = 3 - i$$, what is $$z_1$$ \cdot $$z_2$$?

Accepted Answer

$$5 + 5i$$

Question 16

Divide $$6 + 8i by$$ $$2 - i$$ and write the result in standard form.

Accepted Answer

$$4 + 4i$$

Question 17

Which of the following best describes the imaginary unit $$i$$?

Accepted Answer

$$i is $$defined as $$\sqrt{-1}$$

Question 18

A physicist models a wave using the complex number $$5i. $$What is the real part of this number?

Accepted Answer

$$0$$

Complex Numbers: Definitions, Operations, and Examples

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