Question 1

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

Accepted Answer

$$a + bi$$

Question 2

What is the sum of $$ (3 + 4i) + (2 - 5i) $$?

Accepted Answer

$$5 - i$$

Question 3

Which of the following is the product of $$ (2 + 3i)(1 - 4i) $$?

Accepted Answer

$$14 - 5i$$

Question 4

What is the complex conjugate of $$ 7 - 2i $$?

Accepted Answer

$$7 + 2i$$

Question 5

Divide and express in standard form: $$ \frac{5 + 2i}{1 - 3i} $$

Accepted Answer

$$-\frac{1}{10} + \frac{17}{10}i$$

Question 6

What is the principal square root of $$-49$$?

Accepted Answer

$$7i$$

Question 7

Solve the quadratic equation $$x^2 + 4 = 0$ for x$.

Accepted Answer

$$x = 2i,\ x = -2i$$

Question 8

Which of the following is a pure imaginary number?

Accepted Answer

$$0 + 5i$$

Question 9

If $$z = 4 + 3i$$, what is $$z \cdot \overline{z}$$?

Accepted Answer

$$25$$

Question 10

A certain electrical circuit has an impedance of $$6 - 8i$$ ohms. What is the magnitude of the impedance?

Accepted Answer

$$10$$

Question 11

Which operation is used to rationalize the denominator when dividing complex numbers?

Accepted Answer

Multiply numerator and denominator by the conjugate of the denominator

Question 12

What is $$\sqrt{-16} + \sqrt{-9} in $$standard form?

Accepted Answer

$$4i + 3i = 7i$$

Question 13

If $$a$$ and $$b$$ are real numbers, which of the following is always true for the complex number $$a + bi$$?

Accepted Answer

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

Question 14

Which of the following best describes the set of all complex numbers?

Accepted Answer

All numbers of the form $$a + bi$$ where $$a$$ and $$b$$ are real numbers

Question 15

A quadratic equation $$x^2 + 2x + 5 = 0$ is solved using the quadratic formula. What are the solutions?

Accepted Answer

$$x = -1 + 2i,\ x = -1 - 2i$$

Complex Numbers: Operations and Applications (Precalculus, Ch. 2.1)

Study Guide - Practice Questions