Question 1

Write the expression $$\frac{8}{3-4i} in $$the standard form $$a + bi.$$

Accepted Answer

$$\frac{24}{25} + \frac{32}{25}i$$

Question 2

Simplify $$-3i(-9 + 8i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$24 + 27i$$

Question 3

Multiply and simplify: $$(-9 + 2i)(3 + i).$$

Accepted Answer

$$-29 - 3i$$

Question 4

Find the midpoint of the line segment joining $$P_1 = (4$$, 3)$$ and P_2$ = (6, 5).$$

Accepted Answer

$$(5, 4)$$

Question 5

Solve the equation $$|x| = -7 in $$the set of real numbers.

Accepted Answer

No solution

Question 6

What is the standard form of the equation of a circle with radius $$r = 4$$ and center $$(h, k) = (0, 0)$$?

Accepted Answer

$$x^2$$ + $$y^2 = 16$

Question 7

Find the center $$(h, k)$$ and radius $$r of $$the circle given by $$x^2 + (y$$ + $$9)^2 = 25$.

Accepted Answer

$$(h, k) = (0, -9);\ r = 5$$

Question 8

Solve the quadratic equation $$x^2 + 8x + 41 = 0$ in the complex number system.

Accepted Answer

$$\{-4 - 5i,\ -4 + 5i\}$$

Question 9

Find the real solutions, if any, of the equation $$x^2 + 7x + 3 = 0$ using the quadratic formula.

Accepted Answer

$$\left\{\frac{-7 - \sqrt{37}}{2},\ \frac{-7 + \sqrt{37}}{2}\right\}$$

Question 10

Given the endpoints of a diameter of a circle $$C(6, -2)$$ and $$D(-4, 4)$$, find the equation of the circle in standard form.

Accepted Answer

$$(x - 1)^2$ + (y - 1)^2$ = 34$$

Question 11

Which of the following graphs correctly represents the circle with center $$(0, 5)$$ and radius $$2$$?

Accepted Answer

Image 7

Question 12

Find the distance between the points $$P_1 = (-3$$, 1)$$ and P_2$ = (-8, 13).$$

Accepted Answer

$$13$$

Question 13

Solve the equation $$|x + 9| = 6.$$

Accepted Answer

$$\{-15, -3\}$$

Question 14

Which of the following is the standard form of the equation of a circle with center $$(6, 5)$$ and radius $$3$$?

Accepted Answer

$$(x - 6)^2$ + (y - 5)^2$ = 9$$

Question 15

Solve the equation $$x^2 + 64 = 0$ in the complex number system.

Accepted Answer

$$\{-8i, 8i\}$$

Question 16

Name the quadrant in which the point $$(-5, 16) is $$located.

Accepted Answer

Quadrant II

Question 17

A circle has the equation $$(x - 2)^2$ + (y + 8)^2$ = 16. $$What are its center and radius?

Accepted Answer

$$(h, k) = (2, -8);\ r = 4$$

Question 18

Which of the following graphs shows a circle with center $$(0, -5)$$ and radius $$3$$?

Accepted Answer

Image 16

Question 19

Solve the equation $$|x - 8| = 0.$$

Accepted Answer

$$\{8\}$$

Question 20

Find the distance between the points $$P_1 = (-7$$, -5)$$ and P_2$ = (2, -2).$$

Accepted Answer

$$\sqrt{90}$$

Precalculus Exam 1 Review: Circles, Complex Numbers, and Coordinate Geometry

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