Test your basic knowledge |

CLEP General Mathematics: Complex Numbers

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. 4th. Rule of Complex Arithmetic
Affix
z1 ^ (z2)
cosh²y - sinh²y
(a + bi) = (c + bi) = (a + c) + ( b + d)i

2. Derives z = a+bi
Polar Coordinates - sin?
Euler Formula
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Complex Numbers: Multiply

3. A complex number and its conjugate
imaginary
ln z
|z-w|
conjugate pairs

4. Real and imaginary numbers
interchangeable
ln z
Any polynomial O(xn) - (n > 0)
complex numbers

5. 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
Imaginary Unit
i^2 = -1
Polar Coordinates - Multiplication
subtracting complex numbers

6. A number that cannot be expressed as a fraction for any integer.
Irrational Number
conjugate
Complex Multiplication
point of inflection

7. V(zz*) = v(a² + b²)
Argand diagram
zz*
Complex Numbers: Multiply
|z| = mod(z)

8. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Roots of Unity
four different numbers: i - -i - 1 - and -1.
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
i^3

9. y / r
Polar Coordinates - sin?
z1 / z2
multiplying complex numbers
radicals

10. E ^ (z2 ln z1)
a + bi for some real a and b.
i^3
z1 ^ (z2)
i²

11. Any number not rational
How to find any Power
Rules of Complex Arithmetic
real
irrational

12. Cos n? + i sin n? (for all n integers)
Field
Rational Number
radicals
(cos? +isin?)n

13. ? = -tan?
zz*
imaginary
Polar Coordinates - Arg(z*)
point of inflection

14. ½(e^(iz) + e^(-iz))
cos z
Complex numbers are points in the plane
Complex Number Formula
conjugate

15. E^(ln r) e^(i?) e^(2pin)
real
Absolute Value of a Complex Number
Roots of Unity
e^(ln z)

16. (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
z1 / z2
How to solve (2i+3)/(9-i)
De Moivre's Theorem
integers

17. 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

18. (a + bi)(c + bi) =
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - Arg(z*)
four different numbers: i - -i - 1 - and -1.
Polar Coordinates - z?¹

19. V(x² + y²) = |z|
Polar Coordinates - r
irrational
v(-1)
Polar Coordinates - sin?

20. (a + bi) = (c + bi) =
(a + c) + ( b + d)i
Liouville's Theorem -
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
For real a and b - a + bi = 0 if and only if a = b = 0

21. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
Any polynomial O(xn) - (n > 0)
Imaginary number
rational
ln z

22. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
multiplying complex numbers
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Integers
conjugate pairs

23. A plot of complex numbers as points.
cos z
(a + c) + ( b + d)i
standard form of complex numbers
Argand diagram

24. A + bi
standard form of complex numbers
For real a and b - a + bi = 0 if and only if a = b = 0
x-axis in the complex plane
Polar Coordinates - Arg(z*)

25. (e^(-y) - e^(y)) / 2i = i sinh y
v(-1)
How to find any Power
x-axis in the complex plane
sin iy

26. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
conjugate
Polar Coordinates - z
Polar Coordinates - z?¹

27. All numbers
Imaginary Numbers
(a + bi) = (c + bi) = (a + c) + ( b + d)i
i^2 = -1
complex

28. R^2 = x
the complex numbers
Square Root
Complex Numbers: Add & subtract
Complex Subtraction

29. Given (4-2i) the complex conjugate would be (4+2i)
Complex Conjugate
Affix
(cos? +isin?)n
Complex Division

30. When two complex numbers are multipiled together.
non-integers
Polar Coordinates - z
Complex Multiplication
i^3

31. For real a and b - a + bi =
0 if and only if a = b = 0
Complex Conjugate
complex numbers
radicals

32. Multiply moduli and add arguments
rational
natural
Euler Formula
Polar Coordinates - Multiplication

33. 1
Imaginary Numbers
i^0
conjugate pairs
i^2

34. A subset within a field.
Complex Subtraction
Irrational Number
Subfield
Polar Coordinates - Division

35. 3
natural
irrational
i^3
zz*

36. 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

37. We can also think of the point z= a+ ib as
Absolute Value of a Complex Number
the vector (a -b)
Subfield
point of inflection

38. When two complex numbers are divided.
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Division
transcendental
Rules of Complex Arithmetic

39. In this amazing number field every algebraic equation in z with complex coefficients
i^4
x-axis in the complex plane
complex
has a solution.

40. When two complex numbers are subtracted from one another.
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Complex Subtraction
a + bi for some real a and b.
four different numbers: i - -i - 1 - and -1.

41. 3rd. Rule of Complex Arithmetic
v(-1)
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
Polar Coordinates - Multiplication

42. To simplify a complex fraction
adding complex numbers
cosh²y - sinh²y
Complex numbers are points in the plane
multiply the numerator and the denominator by the complex conjugate of the denominator.

43. I
Polar Coordinates - r
i^1
transcendental
z + z*

44. Every complex number has the 'Standard Form':
Complex Division
a + bi for some real a and b.
Roots of Unity
four different numbers: i - -i - 1 - and -1.

45. (e^(iz) - e^(-iz)) / 2i
i²
sin z
Irrational Number
The Complex Numbers

46. All the powers of i can be written as
four different numbers: i - -i - 1 - and -1.
Complex Numbers: Multiply
'i'
i²

47. 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.
Every complex number has the 'Standard Form': a + bi for some real a and b.
How to find any Power
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Polar Coordinates - Multiplication

48. 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.
Complex numbers are points in the plane
the complex numbers
z1 / z2
Complex Exponentiation

49. xpressions such as ``the complex number z'' - and ``the point z'' are now
interchangeable
i^2
Polar Coordinates - Multiplication by i
the complex numbers

50. A number that can be expressed as a fraction p/q where q is not equal to 0.
z + z*
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Complex Multiplication
Rational Number

Sorry!:) No result found.

Can you answer 50 questions in 15 minutes?

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

Test your basic knowledge |

CLEP General Mathematics: 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

Certifications

IT Skills

Business Skills

Soft Skills

Vocabulary

Languages

Engineering

Health Sciences

English

Math

Other Major Subjects

Browse all subjects

Browse all tests

Most popular tests