Question 1

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

Accepted Answer

$$a + bi$$

Question 2

What is the value of $$i^{23}$$?

Accepted Answer

$$i$$

Question 3

Simplify the expression $$\sqrt{-48} / \sqrt{24}.$$

Accepted Answer

$$i \sqrt{2}$$

Question 4

If $$z = 5 - 4i$$ and $$w = 7 - 2i$$, what is $$z \cdot w$$?

Accepted Answer

$$27 - 38i$$

Question 5

Which of the following statements about the graph of $$P(x) = a(x-h)^2$ + k is $$FALSE?

Accepted Answer

If $$|a| \u003c 1$$, the parabola is narrower than $$y = x^2$.

Question 6

A ball is projected upward from a height of 100 feet with an initial velocity of 80 ft/s. Its height after $$t$$ seconds is $$s(t) = -16t^2$ + 80t + 100. $$What is the maximum height reached by the ball?

Accepted Answer

$$200$$ feet

Question 7

What is the solution set of $$x^2 = -25$?

Accepted Answer

$$\{5i, -5i\}$$

Question 8

Given the quadratic function $$P(x) = 2x^2$ + 4x + 6$$, what are the coordinates of its vertex?

Accepted Answer

$$(-1, 4)$$

Question 9

A farmer has 120 feet of fencing and uses one side of a barn as part of a rectangular enclosure. If $$x is $$the length of one side perpendicular to the barn, what is the maximum area that can be enclosed?

Accepted Answer

$$1800$$ square feet

Question 10

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

Accepted Answer

$$3 - 7i$$

Question 11

Solve the quadratic equation $$x^2 - 4x + 2 = 0$ using the quadratic formula.

Accepted Answer

$$2 \pm \sqrt{2}$$

Question 12

Which of the following best describes the number and type of solutions for the equation $$x^2 + 4x + 8 = 0$?

Accepted Answer

Two complex solutions

Question 13

If $$P(x) = -x^2$ - 6x - 8$$, what is the maximum value of $$P(x)$$?

Accepted Answer

$$1$$

Question 14

Which of the following intervals is the solution set for the inequality $$x^2 - x - 12$$ \u003c 0$$?

Accepted Answer

$$( -3, 4 )$$

Question 15

Given $$a \u003e 0$$, which of the following is true for $$\sqrt{-a}$$?

Accepted Answer

$$i \sqrt{a}$$

Question 16

If $$P(x) = a(x-h)^2$ + k$$ and $$a \u003c 0$$, which statement is true?

Accepted Answer

The vertex is the maximum point of the graph.

Question 17

What is the sum $$(3 - 4i) + (-2 + 6i)$$?

Accepted Answer

$$1 + 2i$$

Question 18

Which of the following is the product $$(a + bi)(a - bi)$$?

Accepted Answer

$$a^2$$ + $$b^2$$

Question 19

A quadratic function has its vertex at $$(2, -3)$$ and passes through $$(8, 69). $$What is its equation in standard form?

Accepted Answer

$$P(x) = 2x^2$ - 8x + 5$$

Question 20

Which of the following best describes the discriminant $$b^2 - 4ac$ of a quadratic equation?

Accepted Answer

It determines the number and type of solutions.

Complex Numbers in Precalculus: Definitions, Operations, and Properties

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