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. (a + bi)(c + bi) =
Subfield
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
|z| = mod(z)
Rational Number
2. (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
How to multiply complex nubers(2+i)(2i-3)
i^2 = -1
Absolute Value of a Complex Number
z + z*
3. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
4. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of
the complex numbers
Absolute Value of a Complex Number
Square Root
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
5. The square root of -1.
adding complex numbers
Imaginary Unit
point of inflection
Imaginary Numbers
6. I
x-axis in the complex plane
i^0
Irrational Number
v(-1)
7. 2ib
z - z*
cos iy
conjugate
x-axis in the complex plane
8. A plot of complex numbers as points.
i^0
cosh²y - sinh²y
Argand diagram
Affix
9. Rotates anticlockwise by p/2
(cos? +isin?)n
rational
sin z
Polar Coordinates - Multiplication by i
10. Given (4-2i) the complex conjugate would be (4+2i)
e^(ln z)
Complex Conjugate
i^4
rational
11. The reals are just the
x-axis in the complex plane
(a + bi) = (c + bi) = (a + c) + ( b + d)i
z + z*
Every complex number has the 'Standard Form': a + bi for some real a and b.
12. 4th. Rule of Complex Arithmetic
How to solve (2i+3)/(9-i)
ln z
x-axis in the complex plane
(a + bi) = (c + bi) = (a + c) + ( b + d)i
13. y / r
Polar Coordinates - sin?
zz*
multiplying complex numbers
Rules of Complex Arithmetic
14. 3rd. Rule of Complex Arithmetic
Imaginary Unit
For real a and b - a + bi = 0 if and only if a = b = 0
Polar Coordinates - sin?
i^2 = -1
15. Every complex number has the 'Standard Form':
a + bi for some real a and b.
How to add and subtract complex numbers (2-3i)-(4+6i)
|z| = mod(z)
De Moivre's Theorem
16. R^2 = x
Absolute Value of a Complex Number
Polar Coordinates - Arg(z*)
Square Root
0 if and only if a = b = 0
17. To simplify the square root of a negative number
Argand diagram
Roots of Unity
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
z + z*
18. 2nd. Rule of Complex Arithmetic
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
19. V(x² + y²) = |z|
Polar Coordinates - Multiplication by i
Polar Coordinates - r
z1 ^ (z2)
non-integers
20. 1. i^2 = -1 2. Every complex number has the 'Standard Form': a + bi for some real a and b. 3. For real a and b - a + bi = 0 if and only if a = b = 0 4. (a + bi) = (c + bi) = (a + c) + ( b + d)i 5. (a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc
Rules of Complex Arithmetic
Polar Coordinates - Multiplication by i
Complex Multiplication
How to add and subtract complex numbers (2-3i)-(4+6i)
21. 5th. Rule of Complex Arithmetic
Roots of Unity
ln z
Polar Coordinates - cos?
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
22. 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
Liouville's Theorem -
z1 / z2
Complex Numbers: Add & subtract
i^1
23. No i
Complex Multiplication
cos iy
real
integers
24. A complex number and its conjugate
conjugate pairs
Argand diagram
cos z
Complex Multiplication
25. When two complex numbers are subtracted from one another.
the vector (a -b)
natural
Complex Subtraction
Real and Imaginary Parts
26. R?¹(cos? - isin?)
Polar Coordinates - z?¹
(cos? +isin?)n
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Euler Formula
27. 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
28. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Absolute Value of a Complex Number
cosh²y - sinh²y
Any polynomial O(xn) - (n > 0)
-1
29. If z= a+bi is a complex number and a and b are real - we say that a is the real part of z and that b is the imaginary part of z
|z-w|
Real and Imaginary Parts
zz*
standard form of complex numbers
30. A subset within a field.
multiply the numerator and the denominator by the complex conjugate of the denominator.
Imaginary Unit
Subfield
point of inflection
31. E ^ (z2 ln z1)
four different numbers: i - -i - 1 - and -1.
0 if and only if a = b = 0
z1 ^ (z2)
'i'
32. z1z2* / |z2|²
z1 / z2
Subfield
standard form of complex numbers
Polar Coordinates - Multiplication
33. To simplify a complex fraction
four different numbers: i - -i - 1 - and -1.
zz*
Polar Coordinates - r
multiply the numerator and the denominator by the complex conjugate of the denominator.
34. A number that cannot be expressed as a fraction for any integer.
rational
Euler's Formula
conjugate
Irrational Number
35. Cos n? + i sin n? (for all n integers)
real
Imaginary number
(cos? +isin?)n
Roots of Unity
36. 1
cos z
Every complex number has the 'Standard Form': a + bi for some real a and b.
i^4
z - z*
37. We can also think of the point z= a+ ib as
the vector (a -b)
Polar Coordinates - sin?
cos z
complex
38. In this amazing number field every algebraic equation in z with complex coefficients
has a solution.
Every complex number has the 'Standard Form': a + bi for some real a and b.
rational
complex numbers
39. Any number not rational
Euler Formula
Field
Complex Multiplication
irrational
40. The modulus of the complex number z= a + ib now can be interpreted as
Polar Coordinates - r
the distance from z to the origin in the complex plane
-1
rational
41. Real and imaginary numbers
complex numbers
Imaginary number
Any polynomial O(xn) - (n > 0)
Imaginary Unit
42. Equivalent to an Imaginary Unit.
Euler Formula
Imaginary number
conjugate pairs
Any polynomial O(xn) - (n > 0)
43. The complex number z representing a+bi.
Affix
cosh²y - sinh²y
Polar Coordinates - r
For real a and b - a + bi = 0 if and only if a = b = 0
44. (a + bi) = (c + bi) =
real
(a + c) + ( b + d)i
Polar Coordinates - Division
z1 / z2
45. All the powers of i can be written as
four different numbers: i - -i - 1 - and -1.
z1 ^ (z2)
Polar Coordinates - r
Imaginary Unit
46. 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.'
Complex Number
We say that c+di and c-di are complex conjugates.
non-integers
Field
47. xpressions such as ``the complex number z'' - and ``the point z'' are now
Polar Coordinates - z?¹
interchangeable
i²
standard form of complex numbers
48. 1
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Imaginary number
the distance from z to the origin in the complex plane
i^0
49. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
e^(ln z)
'i'
conjugate
-1
50. ½(e^(-y) +e^(y)) = cosh y
Polar Coordinates - z?¹
cos iy
Polar Coordinates - cos?
standard form of complex numbers
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