Question 1

Simplify the following expression and write your answer in the form $$a + bi$$:

$$(2 - i) - (-3 + 5i)$$

Accepted Answer

$$5 - 6i$$

Question 2

Multiply the following complex numbers and write your answer in the form $$a + bi$$:

$$(-4 - 3i)(5 - 6i)$$

Accepted Answer

$$-38 + 9i$$

Question 3

Find the product of the complex number $$\dfrac{3}{4} + \dfrac{1}{4}i$$ and its conjugate. Write your answer as a real number.

Accepted Answer

$$1$$

Question 4

Divide and write your answer in the form $$a + bi$$:

$$\dfrac{11}{1 - i}$$

Accepted Answer

$$\dfrac{11}{2} + \dfrac{11}{2}i$$

Question 5

Write the following expression in the form $$a + bi$$:

$$-\sqrt{81} - \sqrt{-4}$$

Accepted Answer

$$-9 + 2i$$

Question 6

Solve the quadratic equation by factoring:

$$x^2 + 8x + 15 = 0$$

Accepted Answer

$$-3, -5$$

Question 7

Solve the equation using the square root property:

$$4(x - 2)^2 = 180$$

Accepted Answer

$$1 \pm 3\sqrt{5}$$

Question 8

Solve the quadratic equation by completing the square:

$$x^2 - 18x - 2 = 0$$

Accepted Answer

$$9 + \sqrt{83},\ 9 - \sqrt{83}$$

Question 9

Use the discriminant to determine the number and nature of the solutions to the equation:

$$3x^2 - 2x - 4 = 0$$

Accepted Answer

There are two real solutions.

Question 10

Benjamin throws a rock straight up from a cliff 36 ft above the water. The height $$h (in $$feet) after $$t$$ seconds is given by:

$$h = -16t^2 + 36t + 36$$

How long will it take for the rock to hit the water?

Accepted Answer

$$3$$ seconds

Question 11

A kite is flying on 106 ft of string. Its height is 34 ft more than the horizontal distance from the person flying it. How high is the kite above the ground?

Accepted Answer

$$90 ft$$

Question 12

Solve the radical equation:

$$\sqrt{6 - 5x} = 0$$

Accepted Answer

$$x = 1$$

Question 13

Solve the polynomial inequality and express the solution in interval notation:

$$16x^3 \u003e 2x^4 + 24x^2$$

Accepted Answer

$$(2, 6)$$

Question 14

Solve the rational inequality and express the solution in interval notation:

$$\dfrac{x + 2}{x - 5} \leq 0$$

Accepted Answer

$$[-2, 5)$$

Question 15

Find all real solutions to the equation:

$$6x^3 - 10x^2 = -28x$$

Accepted Answer

$$-5, 0, \dfrac{1}{3}$$

Question 16

Solve for $$x$$ using the quadratic formula:

$$4x^2 - x + 8 = 0$$

Accepted Answer

$$\dfrac{1 + i\sqrt{127}}{8},\ \dfrac{1 - i\sqrt{127}}{8}$$

Question 17

Write the following expression in the form $$a + bi$$:

$$-9 - \sqrt{-9/6}$$

Accepted Answer

$$-3/2 + (1/2)i$$

Question 18

Solve the equation by factoring:

$$y^2 - 12y = 0$$

Accepted Answer

$$0, 12$$

Question 19

The sum of the square of a positive number and the square of 3 more than the number is 149. What is the number?

Accepted Answer

$$7$$

College Algebra Chapter 1 Test Review – Step-by-Step Guidance

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