SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
Test your basic knowledge |
CLEP General Mathematics: Complex Numbers
Start Test
Study First
Subjects
:
clep
,
math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'
Absolute Value of a Complex Number
e^(ln z)
Complex Number
Euler Formula
2. For real a and b - a + bi =
Polar Coordinates - r
0 if and only if a = b = 0
Field
i^2 = -1
3. 1
Affix
four different numbers: i - -i - 1 - and -1.
Every complex number has the 'Standard Form': a + bi for some real a and b.
i^2
4. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that
We say that c+di and c-di are complex conjugates.
i^2
Polar Coordinates - z
Every complex number has the 'Standard Form': a + bi for some real a and b.
5. We see in this way that the distance between two points z and w in the complex plane is
ln z
How to find any Power
Imaginary Numbers
|z-w|
6. ½(e^(-y) +e^(y)) = cosh y
has a solution.
i^0
Absolute Value of a Complex Number
cos iy
7. The modulus of the complex number z= a + ib now can be interpreted as
Complex Addition
imaginary
the distance from z to the origin in the complex plane
point of inflection
8. In this amazing number field every algebraic equation in z with complex coefficients
x-axis in the complex plane
has a solution.
transcendental
i^1
9. When two complex numbers are divided.
The Complex Numbers
Argand diagram
rational
Complex Division
10. Where the curvature of the graph changes
Complex Number
Complex Numbers: Add & subtract
Polar Coordinates - sin?
point of inflection
11. 1
i^4
Complex Conjugate
Polar Coordinates - r
irrational
12. I
|z| = mod(z)
multiply the numerator and the denominator by the complex conjugate of the denominator.
sin z
i^1
13. Numbers on a numberline
(cos? +isin?)n
interchangeable
integers
real
14. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
conjugate
multiplying complex numbers
complex numbers
Affix
15. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
16. (e^(-y) - e^(y)) / 2i = i sinh y
Absolute Value of a Complex Number
sin iy
i^2
imaginary
17. ½(e^(iz) + e^(-iz))
e^(ln z)
complex
cos z
Imaginary Numbers
18. E ^ (z2 ln z1)
complex
multiplying complex numbers
cosh²y - sinh²y
z1 ^ (z2)
19. Divide moduli and subtract arguments
Any polynomial O(xn) - (n > 0)
i^3
i^4
Polar Coordinates - Division
20. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8
v(-1)
How to multiply complex nubers(2+i)(2i-3)
the distance from z to the origin in the complex plane
Imaginary Numbers
21. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17
the vector (a -b)
integers
How to solve (2i+3)/(9-i)
Integers
22. All numbers
the complex numbers
imaginary
complex
Polar Coordinates - z
23. 1st. Rule of Complex Arithmetic
How to multiply complex nubers(2+i)(2i-3)
i^2 = -1
Real Numbers
integers
24. To simplify a complex fraction
i^3
Imaginary Numbers
multiply the numerator and the denominator by the complex conjugate of the denominator.
i^1
25. A + bi = z1 c + di = z2 - addition: z1 + z2 = (a + bi) + (c + di) = (a + c) + (b + d)i subtraction: z1 - z2 = (a - c) + (b - d)i
a + bi for some real a and b.
Polar Coordinates - sin?
Complex Numbers: Add & subtract
z + z*
26. 3rd. Rule of Complex Arithmetic
How to solve (2i+3)/(9-i)
Absolute Value of a Complex Number
For real a and b - a + bi = 0 if and only if a = b = 0
the distance from z to the origin in the complex plane
27. 1
i^0
e^(ln z)
Integers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
28. A plot of complex numbers as points.
radicals
Argand diagram
Complex Numbers: Add & subtract
e^(ln z)
29. 4th. Rule of Complex Arithmetic
Real Numbers
(a + bi) = (c + bi) = (a + c) + ( b + d)i
The Complex Numbers
a + bi for some real a and b.
30. Imaginary number
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
31. I^26/4= i^24 x i^2 =-1 so u divide the number by 4 and whatevers left over is the number that its equal to.
subtracting complex numbers
How to find any Power
Integers
Affix
32. I^2 =
sin iy
-1
Complex Number Formula
has a solution.
33. Written as fractions - terminating + repeating decimals
'i'
Any polynomial O(xn) - (n > 0)
rational
Euler's Formula
34. Have radical
Complex Division
e^(ln z)
radicals
Roots of Unity
35. (e^(iz) - e^(-iz)) / 2i
sin z
interchangeable
Complex Number
the distance from z to the origin in the complex plane
36. (a + bi) = (c + bi) =
z1 / z2
Polar Coordinates - Multiplication by i
(a + c) + ( b + d)i
imaginary
37. A complex number and its conjugate
Complex Division
cos iy
i²
conjugate pairs
38. V(zz*) = v(a² + b²)
|z| = mod(z)
multiplying complex numbers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Subfield
39. When two complex numbers are multipiled together.
Imaginary number
How to multiply complex nubers(2+i)(2i-3)
Polar Coordinates - Multiplication by i
Complex Multiplication
40. Not on the numberline
Liouville's Theorem -
non-integers
Real and Imaginary Parts
Complex Numbers: Add & subtract
41. A + bi
-1
standard form of complex numbers
z - z*
Complex Numbers: Multiply
42. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
the complex numbers
(a + c) + ( b + d)i
How to add and subtract complex numbers (2-3i)-(4+6i)
Complex Multiplication
43. Has exactly n roots by the fundamental theorem of algebra
point of inflection
Any polynomial O(xn) - (n > 0)
standard form of complex numbers
cos z
44. A complex number may be taken to the power of another complex number.
has a solution.
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
conjugate
Complex Exponentiation
45. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
46. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Conjugate
conjugate
x-axis in the complex plane
47. The field of all rational and irrational numbers.
Real Numbers
Absolute Value of a Complex Number
interchangeable
We say that c+di and c-di are complex conjugates.
48. A subset within a field.
cos z
i^2
Subfield
radicals
49. Like pi
0 if and only if a = b = 0
|z-w|
transcendental
adding complex numbers
50. When two complex numbers are added together.
Complex Conjugate
Square Root
Complex Addition
Polar Coordinates - Multiplication by i
Sorry!:) No result found.
Can you answer 50 questions in 15 minutes?
Let me suggest you:
Browse all subjects
Browse all tests
Most popular tests
Major Subjects
Tests & Exams
AP
CLEP
DSST
GRE
SAT
GMAT
Certifications
CISSP go to https://www.isc2.org/
PMP
ITIL
RHCE
MCTS
More...
IT Skills
Android Programming
Data Modeling
Objective C Programming
Basic Python Programming
Adobe Illustrator
More...
Business Skills
Advertising Techniques
Business Accounting Basics
Business Strategy
Human Resource Management
Marketing Basics
More...
Soft Skills
Body Language
People Skills
Public Speaking
Persuasion
Job Hunting And Resumes
More...
Vocabulary
GRE Vocab
SAT Vocab
TOEFL Essential Vocab
Basic English Words For All
Global Words You Should Know
Business English
More...
Languages
AP German Vocab
AP Latin Vocab
SAT Subject Test: French
Italian Survival
Norwegian Survival
More...
Engineering
Audio Engineering
Computer Science Engineering
Aerospace Engineering
Chemical Engineering
Structural Engineering
More...
Health Sciences
Basic Nursing Skills
Health Science Language Fundamentals
Veterinary Technology Medical Language
Cardiology
Clinical Surgery
More...
English
Grammar Fundamentals
Literary And Rhetorical Vocab
Elements Of Style Vocab
Introduction To English Major
Complete Advanced Sentences
Literature
Homonyms
More...
Math
Algebra Formulas
Basic Arithmetic: Measurements
Metric Conversions
Geometric Properties
Important Math Facts
Number Sense Vocab
Business Math
More...
Other Major Subjects
Science
Economics
History
Law
Performing-arts
Cooking
Logic & Reasoning
Trivia
Browse all subjects
Browse all tests
Most popular tests