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This document contains 20 multiple choice questions testing concepts in complex numbers and operations. The questions cover topics such as simplifying complex expressions, adding, subtracting and multiplying complex numbers, evaluating complex functions, finding conjugates and inverses, graphing complex numbers on an Argand diagram, and properties of complex exponents.
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Operations
Name_____________________________________________
1. If a > 0, then 2 2
9 16a a equals
[1] 5 a [2] 7a [3] 5a [4] 7a
2. The expression 3 7 4
54a b simplifies to
[1] 3 2 3
3 6a b a [2] 2 3
3 6a b a [3] 6 3 3
54a b a [4] 2 3
3 2a b ab
3. Evaluate:
2 0
2
4 (6 2)
3
[1] -144 [2] 144 [3]
16
9
[4]
16
9
4. Write without negative exponents:
21 3
6a b
[1] 2 6
36a b [2]
2
6
36
a
b
[3] 2 6
36
a b
[4] 3 6
36
a b
5. Evaluate
2
38
x
when x = -27.
[1]
4
9
[2]
2
3
[3]
24 3
27
[4]
4
9
6. Simplify 42
i .
[1] i [2] -i [3] 1 [4] -1
7. Simplify
3
80
4
.
[1] 12 5i [2] 6 5i [3] 3 5i [4] 6 5
8. Add and express in a + bi form: 8 8 10 72
[1] 18 4 5i [2] 18 4 2 [3] 18 4 5 [4] 18 4 2i
9. Subtract 14 - 6i from 28 + 3i.
[1] 42 + 9i [2] 14 - 3i [3] 14 + 9i [4] -14 - 9i
10. Multiply: ( 4 - 5i )( 4 + 5i )
[1] 16 - 25i [2] 16 + 25i [3] 9 [4] 41
1.________
2.________
3.________
4.________
5.________
6.________
7.________
8.________
9.________
10._______](https://image.slidesharecdn.com/quiz1-151205203847-lva1-app6892/85/q1-1-320.jpg)
![All Rights Reserved ©RegentsPrep.org
11. Simplify:
8 3i
i
[1] 3 + 8i [2] 3 - 8i [3] -3 -8i [4] -8 + 3i
12. Simplify:
1 2
3 4
i
i
[1]
1 2
5 5
i [2]
1 2
5 5
i [3]
11 2
25 5
i [4]
11 2
25 5
i
13. What is the multiplicative inverse of
3 3
4 4
i ?
[1]
3 3
4
i
[2]
4
3 3i
[3]
4
3
[4]
3
4
14. Complex numbers are graphed on a set of axes referred to as a(n)__________.
[1] Imaginary Plot [2] Argand Diagram [3] Complex Plot [4] Complex Diagram
15. What is the sum of 5 - 3i and the conjugate of 3 + 2i ?
[1] 8 - i [2] 2 + 5i [3] 8 - 5i [4] 2 - 5i
16. The product of 7
i and 5
i is equivalent to
[1] 1 [2] -1 [3] i [4] -i
17. The expression
36
36
is equivalent to
[1] 6i [2] -i [3] i [4] 5
18. If m > 0, the expression 2m m is equivalent to
[1] 2m [2] 2
2m [3] 2m [4] 2m
19. The complex number c + di is equal to (3 - i)². What is the value of c?
[1] 3 [2] 6 [3] 8 [4] 10
20. If
21
32
( ) 2g x x x
, find g(64).
[1]
5
16
[2]
1 1
168 2
[3] 8 2 16 [4] 20
11._______
12._______
13._______
14._______
15._______
16._______
17._______
18._______
19._______
20._______](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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This document contains the table of contents for a 17 chapter book on introductory mathematical analysis. It lists the chapter numbers and titles. The document also contains two sections of math problems related to topics in algebra such as integers, rational numbers, operations with numbers, and algebraic expressions. The problems are multiple choice or require short solutions showing steps to solve equations or expressions.
31350052 introductory-mathematical-analysis-textbook-solution-manual
This document appears to be the table of contents and problems from Chapter 0 of a mathematics textbook. The table of contents lists 17 chapters and their corresponding page numbers. The problems cover a range of algebra topics including integers, rational numbers, properties of operations, solving equations, and rational expressions. There are over 70 problems presented without solutions for students to work through.
Sol mat haeussler_by_priale
This document appears to be the table of contents and problems from Chapter 0 of a mathematics textbook. The table of contents lists 17 chapters and their corresponding page numbers. The problems cover a range of algebra topics including integers, rational numbers, properties of operations, solving equations, and rational expressions. There are over 70 problems presented without solutions for students to work through.
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This document discusses complex numbers. It defines the imaginary unit i as having the property i^2 = -1. Complex numbers are expressed as a + bi, where a is the real part and bi is the imaginary part. Complex numbers can be added, subtracted, multiplied, and divided following certain properties. They can be plotted on a complex plane with the real component on the x-axis and imaginary component on the y-axis. Powers of i follow a repeating pattern of 1, -1, i, -i with the remainder of dividing the exponent by 4 determining the term. Students are assigned practice problems and a quiz on previous concepts.
Lista Plantão 03 - 7º ano
The document contains a list of math problems involving expressions, multiplication, and division. It asks the student to solve expressions with variables, perform multiplication and division with positive and negative numbers, and identify properties like the commutative property being applied. There are over 70 individual math problems and questions for the student to complete.
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The document describes several sorting algorithms:
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pot fracciones log etc.pdf
The document provides examples of solved exercises involving fractions, powers, and logarithms. It includes operations with fractions such as addition, subtraction, multiplication, and division. It also covers operations with powers such as evaluating expressions with exponents, multiplying and dividing terms with the same base, and rationalizing radicals. Finally, it asks to express sets of real numbers using interval notation and represent them on the real number line. The exercises cover basic but important skills in algebra.
Math 5
1. The document discusses addition, subtraction, and multiplication of numbers with 7, 8, or 9 digits. It explains that the placement of ones, thousands, and millions should be under their respective places.
2. Examples are provided to demonstrate addition, subtraction, and multiplication of multi-digit numbers. Diagrams are used to illustrate multiplication.
3. The concepts of reciprocals, fractions, and order of operations are also explained through examples. Verification of equality between expressions is demonstrated.
Lista plantão 08 - 7º ano
The document contains a math worksheet for a 7th grade student with various algebra problems involving operations with positive and negative numbers and exponents. There are 6 sections with multiple parts to each section involving simplifying expressions, performing operations, and associating values. The student is asked to show their work and provide the answer for each problem.
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The document discusses properties of matrix addition and scalar multiplication. It explains that to add matrices, we add corresponding elements and the matrices must have the same dimensions. Scalar multiplication involves multiplying each element of the matrix by the scalar. Some key properties covered are:
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Lista plantão 05 - 7º ano
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q1
- 1. All Rights Reserved ©RegentsPrep.org Operations Name_____________________________________________ 1. If a > 0, then 2 2 9 16a a equals [1] 5 a [2] 7a [3] 5a [4] 7a 2. The expression 3 7 4 54a b simplifies to [1] 3 2 3 3 6a b a [2] 2 3 3 6a b a [3] 6 3 3 54a b a [4] 2 3 3 2a b ab 3. Evaluate: 2 0 2 4 (6 2) 3 [1] -144 [2] 144 [3] 16 9 [4] 16 9 4. Write without negative exponents: 21 3 6a b [1] 2 6 36a b [2] 2 6 36 a b [3] 2 6 36 a b [4] 3 6 36 a b 5. Evaluate 2 38 x when x = -27. [1] 4 9 [2] 2 3 [3] 24 3 27 [4] 4 9 6. Simplify 42 i . [1] i [2] -i [3] 1 [4] -1 7. Simplify 3 80 4 . [1] 12 5i [2] 6 5i [3] 3 5i [4] 6 5 8. Add and express in a + bi form: 8 8 10 72 [1] 18 4 5i [2] 18 4 2 [3] 18 4 5 [4] 18 4 2i 9. Subtract 14 - 6i from 28 + 3i. [1] 42 + 9i [2] 14 - 3i [3] 14 + 9i [4] -14 - 9i 10. Multiply: ( 4 - 5i )( 4 + 5i ) [1] 16 - 25i [2] 16 + 25i [3] 9 [4] 41 1.________ 2.________ 3.________ 4.________ 5.________ 6.________ 7.________ 8.________ 9.________ 10._______
- 2. All Rights Reserved ©RegentsPrep.org 11. Simplify: 8 3i i [1] 3 + 8i [2] 3 - 8i [3] -3 -8i [4] -8 + 3i 12. Simplify: 1 2 3 4 i i [1] 1 2 5 5 i [2] 1 2 5 5 i [3] 11 2 25 5 i [4] 11 2 25 5 i 13. What is the multiplicative inverse of 3 3 4 4 i ? [1] 3 3 4 i [2] 4 3 3i [3] 4 3 [4] 3 4 14. Complex numbers are graphed on a set of axes referred to as a(n)__________. [1] Imaginary Plot [2] Argand Diagram [3] Complex Plot [4] Complex Diagram 15. What is the sum of 5 - 3i and the conjugate of 3 + 2i ? [1] 8 - i [2] 2 + 5i [3] 8 - 5i [4] 2 - 5i 16. The product of 7 i and 5 i is equivalent to [1] 1 [2] -1 [3] i [4] -i 17. The expression 36 36 is equivalent to [1] 6i [2] -i [3] i [4] 5 18. If m > 0, the expression 2m m is equivalent to [1] 2m [2] 2 2m [3] 2m [4] 2m 19. The complex number c + di is equal to (3 - i)². What is the value of c? [1] 3 [2] 6 [3] 8 [4] 10 20. If 21 32 ( ) 2g x x x , find g(64). [1] 5 16 [2] 1 1 168 2 [3] 8 2 16 [4] 20 11._______ 12._______ 13._______ 14._______ 15._______ 16._______ 17._______ 18._______ 19._______ 20._______