Question 1

Which of the following is the correct expression for $$\sqrt{-48} in $$terms of $$i$$?

Accepted Answer

$$4i\sqrt{3}$$

Question 2

A quadratic function $$f(x)$$ has no real zeros. What does this imply about its graph and its solutions?

Accepted Answer

The graph does not cross the $$x-$$axis, and the solutions are complex numbers.

Question 3

Simplify the following expression: $$(3 - 7i)^2$

Accepted Answer

$$-40 - 42i$$

Question 4

Which of the following statements about complex numbers is TRUE?

Accepted Answer

The product of a complex number and its conjugate is always a real number.

Question 5

Express $$\sqrt{-64} in $$terms of $$i.$$

Accepted Answer

$$8i$$

Question 6

What is the result of $$(1 + 2i)(1 + 3i)$$?

Accepted Answer

$$-5 + 5i$$

Question 7

Which of the following is a pure imaginary number?

Accepted Answer

$$0 + 5i$$

Question 8

Simplify $$i^{23}.$$

Accepted Answer

$$-i$$

Question 9

A medical imaging device uses the number $$2 - 5i in a $$calculation. To divide by $$1 - 6i$$, what is the simplified result?

Accepted Answer

$$\frac{32 + 7i}{37}$$

Question 10

Which property is NOT generally true for the addition of complex numbers?

Accepted Answer

Multiplicative inverse

Question 11

If $$z = 5 + 7i$$, what is $$z \cdot \overline{z}$$, where $$\overline{z} is $$the conjugate of $$z$$?

Accepted Answer

$$74$$

Question 12

Which of the following best describes the imaginary part of the complex number $$a + bi$$?

Accepted Answer

$$b$$

Question 13

A chemical reaction is modeled by the equation $$x^2 + 4 = 0$. What are the solutions?

Accepted Answer

$$2i$$ and $$-2i$$

Question 14

Simplify $$\sqrt{-16} \cdot \sqrt{-25}.$$

Accepted Answer

$$-20$$

Question 15

Which of the following is the conjugate of $$14 - 5i$$?

Accepted Answer

$$14 + 5i$$

Question 16

A signal in an electrical circuit is represented by $$8i. $$What is the product of $$8i$$ and $$-8i$$?

Accepted Answer

$$64$$

Question 17

Which of the following is NOT a valid property of complex number addition?

Accepted Answer

Multiplicative identity

Question 18

If $$a + bi is a $$complex number, which of the following is always true?

Accepted Answer

$$(a + bi) + (a - bi) is a $$real number.

Question 19

Simplify $$i^{36}.$$

Accepted Answer

$$1$$

Question 20

A quadratic equation in a physics problem has solutions $$x = 3 + 4i$$ and $$x = 3 - 4i. $$What is the sum of the solutions?

Accepted Answer

$$6$$

Complex Numbers in Precalculus: Definitions, Operations, and Examples

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