Question 1

Perform the addition or subtraction and write the result in standard form. ​​ $( 12 - i ) - ( 7 - i )$ ​

Accepted Answer

A) 5 
B) 7 
C) 9 
D) 8 
E) ​6 
A) 5 
B) 7 
C) 9 
D) 8 
E) ​6

Question 2

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $2 - 14 i$ ​

Accepted Answer

A) ​ $2 + 14 i , 196$ 
B) ​ $2 - 14 i , 196$ 
C) ​ $2 - 14 i , 200$ 
D) ​ $- 2 + 14 i , 196$ 
E) ​ $2 + 14 i , 200$ 
A) ​ $2 + 14 i , 196$ 
B) ​ $2 - 14 i , 196$ 
C) ​ $2 - 14 i , 200$ 
D) ​ $- 2 + 14 i , 196$ 
E) ​ $2 + 14 i , 200$

Question 3

Write the complex number in standard form.​ $8 + \sqrt { - 25 }$ ​

Accepted Answer

A) ​ $8 + 25 i$ 
B) ​ $11 - 8 i$ 
C) ​ $11 + 8 i$ 
D) ​ $8 - 5 i$ 
E) ​ $8 + 5 i$ 
A) ​ $8 + 25 i$ 
B) ​ $11 - 8 i$ 
C) ​ $11 + 8 i$ 
D) ​ $8 - 5 i$ 
E) ​ $8 + 5 i$

Question 4

Write the quotient in standard form.​ $\frac { 4 + i } { 4 - i }$ ​

Accepted Answer

A)  $\frac { 15 } { 17 }$ - $\frac { 8 } { 17 }$ i 
B)  $\frac { 15 } { 17 }$ + $\frac { 17 } { 8 }$ i 
C)  $\frac { 15 } { 17 }$ + $\frac { 8 } { 17 }$ i 
D)  $\frac { 17 } { 15 }$ + $\frac { 17 } { 8 }$ i 
E)  $\frac { 17 } { 15 }$ + $\frac { 8 } { 17 }$ i 
A)  $\frac { 15 } { 17 }$ - $\frac { 8 } { 17 }$ i 
B)  $\frac { 15 } { 17 }$ + $\frac { 17 } { 8 }$ i 
C)  $\frac { 15 } { 17 }$ + $\frac { 8 } { 17 }$ i 
D)  $\frac { 17 } { 15 }$ + $\frac { 17 } { 8 }$ i 
E)  $\frac { 17 } { 15 }$ + $\frac { 8 } { 17 }$ i

Question 5

Simplify the complex number and write it in standard form.​ $3 i ^ { 2 } - 7 i ^ { 3 }$ ​

Accepted Answer

A) ​ $- 7 + 3 i$ 
B) ​ $3 + 7 i$ 
C) ​ $- 3 - 7 i$ 
D) ​ $- 3 + 7 i$ 
E) ​ $3 - 7 i$ 
A) ​ $- 7 + 3 i$ 
B) ​ $3 + 7 i$ 
C) ​ $- 3 - 7 i$ 
D) ​ $- 3 + 7 i$ 
E) ​ $3 - 7 i$

Question 6

Perform the operation and write the result in standard form.​ $$( 4 + 5 i ) ^ { 2 }$$ ​

Accepted Answer

A)  $- 9 + 40 i$ 
B)  $- 9 - 40 i$ 
C)  $9 - 40 i$ 
D)  $- 40 + 9 i$ 
E)  $9 + 40 i$ 
A)  $- 9 + 40 i$ 
B)  $- 9 - 40 i$ 
C)  $9 - 40 i$ 
D)  $- 40 + 9 i$ 
E)  $9 + 40 i$

Question 7

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $- 1 - \sqrt { 7 } i$ ​

Accepted Answer

A) ​ $- 1 + \sqrt { 7 } i , 100$ 
B) ​ $- 1 + \sqrt { 7 } i , 8$ 
C) ​ $- 1 + \sqrt { 7 } i , - 6$ 
D) ​ $1 - \sqrt { 7 i } , 100$ 
E) ​ $1 + \sqrt { 7 } i , 8$ 
A) ​ $- 1 + \sqrt { 7 } i , 100$ 
B) ​ $- 1 + \sqrt { 7 } i , 8$ 
C) ​ $- 1 + \sqrt { 7 } i , - 6$ 
D) ​ $1 - \sqrt { 7 i } , 100$ 
E) ​ $1 + \sqrt { 7 } i , 8$

Question 8

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer.
​
(3 - 8i)+ (10 + 5i)

Accepted Answer

The answer of Do the operation and express the answer...

Question 9

Write the quotient in standard form.​ $\frac { 11 } { 1 - i }$ ​

Accepted Answer

A) ​ $\frac { 11 } { 2 + i }$ 
B) ​ $\frac { 11 } { 2 } i$ 
C) ​ $\frac { 11 } { 2 - i }$ 
D) ​ $\frac { 11 } { 2 } + \frac { 11 } { 2 } i$ 
E) ​ $\frac { 11 } { 2 } - \frac { 11 } { 2 } i$ 
A) ​ $\frac { 11 } { 2 + i }$ 
B) ​ $\frac { 11 } { 2 } i$ 
C) ​ $\frac { 11 } { 2 - i }$ 
D) ​ $\frac { 11 } { 2 } + \frac { 11 } { 2 } i$ 
E) ​ $\frac { 11 } { 2 } - \frac { 11 } { 2 } i$

Question 10

Do the operation and express the answer in a + bi form.​ $( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )$ ​

Accepted Answer

A) - 8 + 14i 
B) 8 + 7i 
C) - 8 + 7i 
D) - 8 - 7i 
E) 8 - 7i 
A) - 8 + 14i 
B) 8 + 7i 
C) - 8 + 7i 
D) - 8 - 7i 
E) 8 - 7i

Question 11

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $5 + 3 i$ ​

Accepted Answer

A) ​ $5 + 3 i , 34$ 
B) ​ $5 - 3 i , 9$ 
C) ​ $5 + 3 i , 9$ 
D) ​ $- 5 - 3 i , 34$ 
E) ​ $5 - 3 i , 34$ 
A) ​ $5 + 3 i , 34$ 
B) ​ $5 - 3 i , 9$ 
C) ​ $5 + 3 i , 9$ 
D) ​ $- 5 - 3 i , 34$ 
E) ​ $5 - 3 i , 34$

Question 12

Simplify the complex number and write it in standard form. ​​ $( 2 i ) ^ { 4 }$ ​

Accepted Answer

A) ​16 
B) ​-16 
C) ​16i 
D) ​​-16i 
E) ​2i 
A) ​16 
B) ​-16 
C) ​16i 
D) ​​-16i 
E) ​2i

Question 13

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $\sqrt { - 39 }$ ​

Accepted Answer

A) -38i,39 
B)  $\sqrt { 39 }$ i,39 
C) 1521i,39 
D) - $\sqrt { 39 }$ i,39 
E) ​-i,39 
A) -38i,39 
B)  $\sqrt { 39 }$ i,39 
C) 1521i,39 
D) - $\sqrt { 39 }$ i,39 
E) ​-i,39

Question 14

Write the complex number in standard form.​ $( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )$ ​

Accepted Answer

A) (24 - $2 \sqrt { 21 }$ )- (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
B) (24 + $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
C) (24 - $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
D) (24 + $2 \sqrt { 21 }$ )- (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
E) (24 + $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ + 4 $\sqrt { 14 }$ )i 
A) (24 - $2 \sqrt { 21 }$ )- (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
B) (24 + $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
C) (24 - $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
D) (24 + $2 \sqrt { 21 }$ )- (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i 
E) (24 + $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ + 4 $\sqrt { 14 }$ )i

Question 15

Write the complex number in standard form.​ $3 - \sqrt { - 30 }$ ​

Accepted Answer

A) 3 + $\sqrt { 30 }$ i​ 
B) 4 + $\sqrt { 30 }$ i 
C) 7 - $\sqrt { 30 }$ i 
D) 3 - $\sqrt { 30 }$ i 
E) 4 - $\sqrt { 30 }$ i 
A) 3 + $\sqrt { 30 }$ i​ 
B) 4 + $\sqrt { 30 }$ i 
C) 7 - $\sqrt { 30 }$ i 
D) 3 - $\sqrt { 30 }$ i 
E) 4 - $\sqrt { 30 }$ i

Question 16

Simplify the complex number and write it in standard form.​ $\frac { 14 } { i ^ { 3 } }$ ​

Accepted Answer

A) ​14i3 
B) ​​-14i3 
C) ​14 
D) ​​​-14i 
E) ​14i 
A) ​14i3 
B) ​​-14i3 
C) ​14 
D) ​​​-14i 
E) ​14i

Question 17

Perform the operation and write the result in standard form.​ $( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )$ ​

Accepted Answer

A) 31 
B) 27 
C) 28 
D) 29 
E) 30 
A) 31 
B) 27 
C) 28 
D) 29 
E) 30

Question 18

Write the complex number in standard form.​ $( \sqrt { - 48 } ) ^ { 2 }$ ​

Accepted Answer

A)  $- \sqrt { 48 }$ 
B) - $$48$$ 
C) ​ $\sqrt { 23 }$ 
D)  $48$ 
E) ​ $\sqrt { 48 }$ 
A)  $- \sqrt { 48 }$ 
B) - $$48$$ 
C) ​ $\sqrt { 23 }$ 
D)  $48$ 
E) ​ $\sqrt { 48 }$

Question 19

Write the complex number in standard form.​ $\sqrt { - 20 } \times \sqrt { - 18 }$ ​ ​

Accepted Answer

A)  $6 \sqrt { 10 }$ 
B)  $- \sqrt { 20 }$ 
C)  - $6 \sqrt { 10 }$ 
D)  $\sqrt { 18 }$ 
E)  $\sqrt { 20 }$ 
A)  $6 \sqrt { 10 }$ 
B)  $- \sqrt { 20 }$ 
C)  - $6 \sqrt { 10 }$ 
D)  $\sqrt { 18 }$ 
E)  $\sqrt { 20 }$

Exam 14: Complex Numbers

Perform the addition or subtraction and write the result in standard form. ​​ (12−i)−(7−i)( 12 - i ) - ( 7 - i )(12−i)−(7−i) ​

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ 2−14i2 - 14 i2−14i ​

Write the complex number in standard form.​ 8+−258 + \sqrt { - 25 }8+−25​ ​

Write the quotient in standard form.​ 4+i4−i\frac { 4 + i } { 4 - i }4−i4+i​ ​

Simplify the complex number and write it in standard form.​ 3i2−7i33 i ^ { 2 } - 7 i ^ { 3 }3i2−7i3 ​

Perform the operation and write the result in standard form.​ (4+5i)2( 4 + 5 i ) ^ { 2 }(4+5i)2 ​

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ −1−7i- 1 - \sqrt { 7 } i−1−7​i ​

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer. ​ (3 - 8i)+ (10 + 5i)

Write the quotient in standard form.​ 111−i\frac { 11 } { 1 - i }1−i11​ ​

Do the operation and express the answer in a + bi form.​ (5−−25)−(2i−3)( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )(5−−25​)−(2i−3) ​

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ 5+3i5 + 3 i5+3i ​

Simplify the complex number and write it in standard form. ​​ (2i)4( 2 i ) ^ { 4 }(2i)4 ​

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ −39\sqrt { - 39 }−39​ ​

Write the complex number in standard form.​ (4+−6)(6−−14)( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )(4+−6​)(6−−14​) ​

Write the complex number in standard form.​ 3−−303 - \sqrt { - 30 }3−−30​ ​

Simplify the complex number and write it in standard form.​ 14i3\frac { 14 } { i ^ { 3 } }i314​ ​

Perform the operation and write the result in standard form.​ (19+8i)(19−8i)( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )(19​+8​i)(19​−8​i) ​

Write the complex number in standard form.​ (−48)2( \sqrt { - 48 } ) ^ { 2 }(−48​)2 ​

Write the complex number in standard form.​ −20×−18\sqrt { - 20 } \times \sqrt { - 18 }−20​×−18​ ​ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Perform the addition or subtraction and write the result in standard form. $( 12 - i ) - ( 7 - i )$

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $2 - 14 i$

Write the complex number in standard form. $8 + \sqrt { - 25 }$

Write the quotient in standard form. $\frac { 4 + i } { 4 - i }$

Simplify the complex number and write it in standard form. $3 i ^ { 2 } - 7 i ^ { 3 }$

Perform the operation and write the result in standard form. $( 4 + 5 i ) ^ { 2 }$

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $- 1 - \sqrt { 7 } i$

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer. (3 - 8i)+ (10 + 5i)

Write the quotient in standard form. $\frac { 11 } { 1 - i }$

Do the operation and express the answer in a + bi form. $( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )$

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $5 + 3 i$

Simplify the complex number and write it in standard form. $( 2 i ) ^ { 4 }$

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $\sqrt { - 39 }$

Write the complex number in standard form. $( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )$

Write the complex number in standard form. $3 - \sqrt { - 30 }$

Simplify the complex number and write it in standard form. $\frac { 14 } { i ^ { 3 } }$

Perform the operation and write the result in standard form. $( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )$

Write the complex number in standard form. $( \sqrt { - 48 } ) ^ { 2 }$

Write the complex number in standard form. $\sqrt { - 20 } \times \sqrt { - 18 }$