Question 1

Which of the following is the correct form for a complex number?

Accepted Answer

$$a + bi$$

Question 2

Given $$z = -6 + i$$, what are the real and imaginary parts of $$z$$?

Accepted Answer

Real: $$-6$$, Imaginary: $$1$$

Question 3

What is the value of $$i^7$$?

Accepted Answer

$$-i$$

Question 4

Simplify $$\sqrt{-44x^2$}$$ assuming $$x is a $$real number.

Accepted Answer

$$2x\sqrt{11}i$$

Question 5

Which of the following numbers is purely imaginary?

Accepted Answer

$$4i$$

Question 6

If $$P(x) = x^2$ + 1$$, what are the roots of $$P(x)$$?

Accepted Answer

$$x = i, x = -i$$

Question 7

What is the value of $$i^{25}$$?

Accepted Answer

$$i$$

Question 8

A medical imaging device uses the number $$z = 2 + 3i in $$its calculations. What is the modulus (absolute value) of $$z$$?

Accepted Answer

$$\sqrt{13}$$

Question 9

Which of the following statements is true about the graph of $$P(x) = x^2$ + 2x + 3$$?

Accepted Answer

It does not cross the $$x-$$axis and has two imaginary roots.

Question 10

Simplify $$\sqrt{-100y^2$z}$$ assuming $$y$$ and $$z$$ are real numbers and $$y \u003e 0.$$

Accepted Answer

$$10y\sqrt{z}i$$

Question 11

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

Accepted Answer

$$1$$

Question 12

A chemical reaction is modeled by the equation $$x^2 - x - 1 = 0$. What type of roots does this equation have?

Accepted Answer

Two distinct real roots

Question 13

Which of the following is NOT a complex number?

Accepted Answer

Question 14

If $$z = 1 - 4i$$, what is the conjugate of $$z$$?

Accepted Answer

$$1 + 4i$$

Question 15

A signal in an electrical circuit is represented by $$z = 2i. $$What is the argument (angle) of $$z in $$radians?

Accepted Answer

$$\frac{\pi}{2}$$

Question 16

What is the result of multiplying $$(2 + 3i)$$ and $$(1 - 4i)$$?

Accepted Answer

$$14 - 5i$$

Question 17

If $$z = -1 - 5i$$, what is $$|z| ($$the modulus of $$z$$)?

Accepted Answer

$$\sqrt{26}$$

Question 18

Which of the following best describes the cyclical nature of powers of $$i$$?

Accepted Answer

Every four powers, the values repeat: $$i, -1, -i, 1$$

Question 19

A quadratic equation $$x^2 + 1 = 0$ is used in a physics simulation. What is the nature of its roots?

Accepted Answer

Both roots are imaginary

Question 20

Evaluate $$33i^{10}.$$

Accepted Answer

$$33$$

Complex Numbers, Imaginary Numbers, and Roots in Precalculus

Study Guide - Practice Questions