Question 1

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

Accepted Answer

$$4\sqrt{3}i$$

Question 2

A quadratic function $$f(x)$$ has no x-intercepts on its graph. What does this indicate about its zeros?

Accepted Answer

The zeros are complex numbers and not real.

Question 3

Simplify $$(8 + 6i) + (3 + 2i).$$

Accepted Answer

$$11 + 8i$$

Question 4

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

Accepted Answer

$$-5 + 5i$$

Question 5

What is the result of $$\sqrt{-16} \cdot \sqrt{-25}$$?

Accepted Answer

$$-20$$

Question 6

Which of the following is the conjugate of the complex number $$-3 + 7i$$?

Accepted Answer

$$-3 - 7i$$

Question 7

Simplify $$i^{58}.$$

Accepted Answer

$$1$$

Question 8

A medical imaging device uses the complex number $$a + bi to $$represent a signal. If $$a = 0$$ and $$b 
eq 0$$, what type of number is this?

Accepted Answer

Pure imaginary number

Question 9

What is the product of $$(5 + 7i)(5 - 7i)$$?

Accepted Answer

$$74$$

Question 10

Simplify $$i^{37}.$$

Accepted Answer

$$i$$

Question 11

A chemical reaction is modeled by the equation $$z = 2 - 5i. To $$divide $$z by$$ $$1 - 6i$$, which of the following is the correct first step?

Accepted Answer

Multiply numerator and denominator by the conjugate of the denominator.

Question 12

Which of the following correctly expresses $$-\sqrt{13} in $$terms of $$i$$?

Accepted Answer

$$-i\sqrt{13}$$

Question 13

Simplify $$(3 - 7i)^2$.

Accepted Answer

$$-40 - 42i$$

Question 14

Which property is NOT generally true for complex numbers?

Accepted Answer

Order property (complex numbers cannot be ordered)

Question 15

If $$i^2 = -1$, what is i^5$?

Accepted Answer

$$i$$

Question 16

A signal in an electrical circuit is represented by $$8i. $$What is its conjugate?

Accepted Answer

$$-8i$$

Question 17

Simplify $$\sqrt{-64}.$$

Accepted Answer

$$-8i$$

Question 18

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

Accepted Answer

The product is always a real number.

Question 19

Simplify $$i^{29}.$$

Accepted Answer

$$-1$$

Question 20

Which of the following is the correct result of $$(4 + 5i) - (6 - 3i)$$?

Accepted Answer

$$-2 + 8i$$

Section 3.1: The Complex Number System – Precalculus Study Notes

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