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. (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 complex numbers
How to solve (2i+3)/(9-i)
conjugate pairs
Polar Coordinates - sin?
2. ½(e^(-y) +e^(y)) = cosh y
radicals
Field
cos iy
Polar Coordinates - cos?
3. (a + bi)(c + bi) =
natural
i^4
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
(cos? +isin?)n
4. A plot of complex numbers as points.
Argand diagram
Polar Coordinates - Arg(z*)
complex numbers
x-axis in the complex plane
5. The complex number z representing a+bi.
We say that c+di and c-di are complex conjugates.
complex
Affix
-1
6. We can also think of the point z= a+ ib as
How to multiply complex nubers(2+i)(2i-3)
the complex numbers
Affix
the vector (a -b)
7. All the powers of i can be written as
Subfield
Polar Coordinates - Multiplication by i
We say that c+di and c-di are complex conjugates.
four different numbers: i - -i - 1 - and -1.
8. 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
9. A + bi
Euler's Formula
non-integers
standard form of complex numbers
Rules of Complex Arithmetic
10. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
Integers
Polar Coordinates - sin?
Argand diagram
Polar Coordinates - Multiplication
11. Derives z = a+bi
imaginary
(a + c) + ( b + d)i
-1
Euler Formula
12. When you add two complex numbers a + bi and c + di - you get the sum of the real parts and the sum of the imaginary parts: (a + bi) + (c + di) = (a + c) + (b + d)i
i^4
Absolute Value of a Complex Number
Polar Coordinates - Division
adding complex numbers
13. Any number not rational
Roots of Unity
a + bi for some real a and b.
irrational
Euler Formula
14. 2ib
z - z*
cos z
i^2 = -1
Irrational Number
15. 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.
Complex Numbers: Add & subtract
How to find any Power
the distance from z to the origin in the complex plane
Square Root
16. R^2 = x
Euler's Formula
Complex Number Formula
Square Root
Polar Coordinates - cos?
17. V(zz*) = v(a² + b²)
Complex Conjugate
cos iy
complex numbers
|z| = mod(z)
18. In the same way that we think of real numbers as being points on a line - it is natural to identify a complex number z=a+ib with the point (a -b) in the cartesian plane.
i^3
Complex numbers are points in the plane
We say that c+di and c-di are complex conjugates.
-1
19. To simplify the square root of a negative number
conjugate pairs
Polar Coordinates - sin?
Field
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
20. Multiply moduli and add arguments
i^0
We say that c+di and c-di are complex conjugates.
Polar Coordinates - Multiplication
For real a and b - a + bi = 0 if and only if a = b = 0
21. 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
a + bi for some real a and b.
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Real and Imaginary Parts
irrational
22. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
the distance from z to the origin in the complex plane
conjugate
Integers
Real Numbers
23. 1
i^0
How to solve (2i+3)/(9-i)
cos z
Euler Formula
24. Have radical
Real Numbers
radicals
(a + bi) = (c + bi) = (a + c) + ( b + d)i
i^2 = -1
25. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
multiplying complex numbers
conjugate pairs
Imaginary number
Polar Coordinates - z
26. Not on the numberline
Complex Number Formula
(a + bi) = (c + bi) = (a + c) + ( b + d)i
non-integers
multiply the numerator and the denominator by the complex conjugate of the denominator.
27. When two complex numbers are divided.
sin z
Field
How to multiply complex nubers(2+i)(2i-3)
Complex Division
28. I
i^1
Subfield
Liouville's Theorem -
Polar Coordinates - Multiplication by i
29. ½(e^(iz) + e^(-iz))
How to multiply complex nubers(2+i)(2i-3)
v(-1)
Complex Numbers: Add & subtract
cos z
30. 1st. Rule of Complex Arithmetic
0 if and only if a = b = 0
i^2 = -1
Complex Numbers: Multiply
Imaginary Numbers
31. To prove that number field every algebraic equation in z with complex coefficients has a solution we need
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
32. xpressions such as ``the complex number z'' - and ``the point z'' are now
irrational
How to add and subtract complex numbers (2-3i)-(4+6i)
cos iy
interchangeable
33. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.
Complex Numbers: Multiply
How to solve (2i+3)/(9-i)
Real Numbers
i^2
34. No i
real
Complex Number
Complex Number Formula
integers
35. We see in this way that the distance between two points z and w in the complex plane is
How to solve (2i+3)/(9-i)
a real number: (a + bi)(a - bi) = a² + b²
Polar Coordinates - Multiplication by i
|z-w|
36. 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
Complex Multiplication
We say that c+di and c-di are complex conjugates.
real
Euler Formula
37. To simplify a complex fraction
multiply the numerator and the denominator by the complex conjugate of the denominator.
-1
Imaginary Numbers
Argand diagram
38. When two complex numbers are multipiled together.
conjugate
Complex Multiplication
Subfield
De Moivre's Theorem
39. 1
Complex Multiplication
a real number: (a + bi)(a - bi) = a² + b²
imaginary
i²
40. When you subtract two complex numbers a + bi and c + di - you get the difference of the real parts and the difference of the imaginary parts: (a + bi) - (c + di) = (a - c) + (b - d)i
subtracting complex numbers
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Field
a + bi for some real a and b.
41. Numbers on a numberline
i^1
Polar Coordinates - Arg(z*)
integers
cos iy
42. (e^(iz) - e^(-iz)) / 2i
Polar Coordinates - Division
sin z
How to solve (2i+3)/(9-i)
z - z*
43. 3
|z-w|
x-axis in the complex plane
We say that c+di and c-di are complex conjugates.
i^3
44. (a + bi) = (c + bi) =
(a + c) + ( b + d)i
How to find any Power
Polar Coordinates - Multiplication
-1
45. The product of an imaginary number and its conjugate is
a real number: (a + bi)(a - bi) = a² + b²
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Square Root
Liouville's Theorem -
46. y / r
Polar Coordinates - sin?
Polar Coordinates - Multiplication
sin iy
Polar Coordinates - z
47. A complex number may be taken to the power of another complex number.
transcendental
Polar Coordinates - z?¹
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Complex Exponentiation
48. Starts at 1 - does not include 0
natural
Complex Number
Imaginary number
complex
49. Like pi
0 if and only if a = b = 0
Euler's Formula
Polar Coordinates - Multiplication
transcendental
50. Has exactly n roots by the fundamental theorem of algebra
Any polynomial O(xn) - (n > 0)
Complex Number
Complex Number Formula
a + bi for some real a and b.
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