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 a complex number?

Accepted Answer

$$a + bi$$, where $$a$$ and $$b$$ are real numbers

Question 3

Which of the following is the result of $$\sqrt{-48}$$ expressed in terms of $$i$$?

Accepted Answer

$$4i\sqrt{3}$$

Question 4

If $$z_1 = 3 - 4i$ and z_2$ = 2 + 6i$$, what is $$z_1$$ + $$z_2$$?

Accepted Answer

$$5 + 2i$$

Question 5

What is the result of multiplying $$(2 - 3i)(3 + 4i)$$?

Accepted Answer

$$18 + i$$

Question 6

Which of the following is the conjugate of the complex number $$6 + 5i$$?

Accepted Answer

$$6 - 5i$$

Question 7

What is the result of dividing $$3 + 2i by$$ $$5 - i in $$standard form $$a + bi$$?

Accepted Answer

$$\frac{13}{26} + \frac{11}{26}i$$

Question 8

Simplify $$i^{15}.$$

Accepted Answer

$$i$$

Question 9

Which of the following statements is true about the product of a complex number and its conjugate?

Accepted Answer

The product is always a real number

Question 10

A medical imaging device uses the complex number $$z = 4 - 3i to $$represent a signal. What is the modulus (absolute value) of $$z$$?

Accepted Answer

$$5$$

Question 11

Which of the following is the result of $$\sqrt{-20} \div \sqrt{-2}$$?

Accepted Answer

$$\sqrt{10}$$

Question 12

If $$a = 0$$ and $$b 
eq 0$$, the complex number $$a + bi is $$called a(n) ________ number.

Accepted Answer

pure imaginary

Question 13

Which of the following is the correct simplification of $$\frac{8 + \sqrt{-128}}{4} in $$standard form $$a + bi$$?

Accepted Answer

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

Question 14

Which property is used when adding complex numbers $$a + bi$$ and $$c + di$$?

Accepted Answer

Add real parts and add imaginary parts

Question 15

A chemical reaction is modeled by the complex number $$z = 2 + 4i. $$What is the argument (angle) $$	heta of$$ $$z in $$radians?

Accepted Answer

$$\arctan(4/2)$$

Question 16

Which of the following is the correct result of $$(3 + 2i) + (9 - 3i)$$?

Accepted Answer

$$12 - i$$

Question 17

Simplify $$i^{23}.$$

Accepted Answer

$$-i$$

Question 18

Which of the following is the result of $$(-2 - 3i)(-2 + 3i)$$?

Accepted Answer

$$13$$

Question 19

A complex number $$z is $$equal to its conjugate only if:

Accepted Answer

Its imaginary part is zero

Question 20

Which of the following is the correct simplification of $$\frac{6 + 2i}{1 + 2i} in $$standard form $$a + bi$$?

Accepted Answer

$$2 - i$$

Basic Concepts and Operations with Complex Numbers

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