Complex numbers Questions and Answers

Solve the equation using the quadratic formula x 7x 12 0

Identify the number of x intercepts and the number of real number solutions for the following quadratic equations 6 N ty x 4

Multiply 3 i 1 4i

A00 41 2 8i

If an arithmetic series has a 2 d 4 and n 29 what is S

Determine fg a if f x 5 2x and g x 3x 1 In the space provided type the coefficients of your final solution in az bx c form 19 2 2

Choose the correct inverse function of f x 2x 4 A B C D f x 2x 8 x 2x 8 f x 2x 8 x 2x 8

Divide 2 15 12 A B C 5 2 15 3 2 15 V12

2 10 points Rewrite the equation for this circle in Standard Form Identify the center and radius of the circle Graph the equation and label four points without using a calculator x 6x y 2y 6 0

Simplify each sum 4 2x 5 6 2x A 1 C 1 5x B 1 x D 3 5x 5 5 2x 6x 3x x A 7x x C 8x x B 15x x D 14x x

x 1 x 15 2x 3x 2 Type a response 1 What is the expression that represents the area of the shaded part of the figure

Simplify each difference 2 3n 6 3n 4n 7 7n A n 4n 12 6n B n 4n 14 6n C n 4n 12 D n 4n 13

State if the given binomial is a factor of the given polynomial 1 11 8x 57x 10x 15x 45x 21 x 7 A No B Yes

SUMMATIVE 3 Divide 8 91x 43x 17x 5 13x 5 A 7x 6x 1 1 13x 5 5 13x 5 3 13x 5 B 7x 6x 3 C 7x 6x 3 D 7x 6x 9 9 2v 35v 90v 28 2v 7 4 2v 7 A v 14v 7 B v 14v 4 C v 14v 4 D v 14v 3 5 2v 7

Simplify 1 2y 2yx y O O O O 16x y15 1 32x 2y15 y x18 4 y x

5 Simplify 2k 8k 7k 6k O O O 14k 2k4 14k 9k 14k 5k 2k4

3 Simplify 6n 4n 3 8n 6n 1 O O O 17n 4 4n 17n 4 12n 4 2

simplify 6a 5a 8 2 4a 6a O O O 2a 14a 1 2a 14a 4 2a 11a 4 2a 11a

In Exercises 11 14 identify all pairs of angles of the given type See Example 3 11 corresponding 12 alternate interior 13 alternate exterior 14 consecutive interior 15 25 and 21 34 17 26 and 213 USING STRUCTURE In Exercises 15 18 classify the angle pair as corresponding alternate interior alternate exterior or consecutive interior angles 56 34 78 56 8 9 10 11 12 13 14 15 16 16 211 and 413 18 42 and 4

Suppose f x 5 Determine and graph four distinct antiderivatives of f 10 8 6 Clear All Draw 10 8 6 4 2 15 4 6 8 10 2 4 6 8 16

3 2 2 3 4 8 7 6 5 The graph of a function y f x is shown Make a sketch of the antiderivative F given that F is continuous and F 0 3 3 2 2 3 15 6 ON M 3

8 x 4 9

f x 3 2x 3 on the interval 4 2

11 9 6 6x 13 8 7 4m 6 15 5 3 3r 9r 17 8m 6 4m 5 19 4 2r 5 4 12 2 10 5 6m 14 10k 4 10 10k 16 7x 7 x 9 18 10 4 4a 4a 20 10 6 5

Multiply 4 21

Subtract 2 7 5 3i

3 5i 6 4i

1 3i 6 4i

Find the complex number for the given radical expression 4 121

4 5i 6 10i

8 3i 7 3i

The complex number 1 2i 3 represents which radical expression below A 1 12 B 1 12 C 1 6 D 1 6

8 15 11 i

16 17i 8 12i

3 51

Find the complex number for the given radical expression 7 20

Identify the real and imaginary parts of the given number Then tell which of the following sets the number belongs to real numbers imaginary numbers and complex numbers 1 i

Simplify i 5

0 9 z

A radical expression is shown below What is the simplified form of this expression 128

State Cayley Hamilton theorem and use it to find A 1 and A4 Where A 1 2 3 2 1 4 L3 1 1

A graphing calculator is recommended In this problem you are asked to find a function that models a real life situation and then use the model to answer questions about the situation Use the guidelines on page 217 to hell A rancher with 700 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle see the figure a Find a function A that models the total area of the four pens Use w to represent the width of the field A W x b Find the largest possible total area of the four pens Xtt Wholes

2 3

That is the simplified form of the expression 180

6 IP Ka

21

2 3i 7

x 24 0

2 31 2 1 2 2 3 2 2 H 2 y sin x 1 Transformation

Write in logarithmic form 5 125 What is the equivalent logarithmic form log 5 Simplify your answers Type integers or fractions