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. ½(e^(iz) + e^(-iz))
Complex numbers are points in the plane
cos z
Polar Coordinates - z?¹
multiplying complex numbers

2. 2a
Polar Coordinates - cos?
De Moivre's Theorem
adding complex numbers
z + z*

3. 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
How to add and subtract complex numbers (2-3i)-(4+6i)
Rules of Complex Arithmetic
i^3
Square Root

4. y / r
Polar Coordinates - Multiplication by i
Polar Coordinates - sin?
Every complex number has the 'Standard Form': a + bi for some real a and b.
four different numbers: i - -i - 1 - and -1.

5. 1
(cos? +isin?)n
i^0
conjugate
Euler Formula

6. E^(ln r) e^(i?) e^(2pin)
Field
irrational
z1 / z2
e^(ln z)

7. 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
Polar Coordinates - Arg(z*)
adding complex numbers
v(-1)

8. I
v(-1)
multiply the numerator and the denominator by the complex conjugate of the denominator.
Argand diagram
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

9. ? = -tan?
Field
interchangeable
Polar Coordinates - Arg(z*)
Complex Conjugate

10. R?¹(cos? - isin?)
Polar Coordinates - z?¹
ln z
a real number: (a + bi)(a - bi) = a² + b²
i^2

11. 1
standard form of complex numbers
i^4
Complex Division
multiplying complex numbers

12. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Roots of Unity
Imaginary Numbers
i^1
Polar Coordinates - z

13. 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

14. When two complex numbers are multipiled together.
Complex Multiplication
Absolute Value of a Complex Number
Real and Imaginary Parts
four different numbers: i - -i - 1 - and -1.

15. A number that can be expressed as a fraction p/q where q is not equal to 0.
Subfield
the complex numbers
Rational Number
sin z

16. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
ln z
conjugate
the complex numbers
cosh²y - sinh²y

17. The product of an imaginary number and its conjugate is
Complex numbers are points in the plane
i^4
Rules of Complex Arithmetic
a real number: (a + bi)(a - bi) = a² + b²

18. Multiply moduli and add arguments
i^2
Polar Coordinates - z
-1
Polar Coordinates - Multiplication

19. xpressions such as ``the complex number z'' - and ``the point z'' are now
Roots of Unity
interchangeable
(a + c) + ( b + d)i
Polar Coordinates - Multiplication by i

20. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
conjugate
a real number: (a + bi)(a - bi) = a² + b²
has a solution.
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

21. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
radicals
Imaginary Unit
Integers
multiplying complex numbers

22. In this amazing number field every algebraic equation in z with complex coefficients
has a solution.
interchangeable
Complex Subtraction
Euler's Formula

23. 5th. Rule of Complex Arithmetic
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Complex Multiplication
Polar Coordinates - Arg(z*)
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

24. I = imaginary unit - i² = -1 or i = v-1
0 if and only if a = b = 0
Polar Coordinates - cos?
Imaginary Numbers
four different numbers: i - -i - 1 - and -1.

25. 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

26. (a + bi)(c + bi) =
Roots of Unity
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Real and Imaginary Parts
Imaginary Unit

27. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
How to add and subtract complex numbers (2-3i)-(4+6i)
Polar Coordinates - z
subtracting complex numbers
Complex Numbers: Multiply

28. To simplify a complex fraction
Rules of Complex Arithmetic
Imaginary Unit
Polar Coordinates - r
multiply the numerator and the denominator by the complex conjugate of the denominator.

29. Every complex number has the 'Standard Form':
a + bi for some real a and b.
point of inflection
the vector (a -b)
a real number: (a + bi)(a - bi) = a² + b²

30. Imaginary number

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

31. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
-1
Imaginary Numbers
multiplying complex numbers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

32. The reals are just the
Field
Liouville's Theorem -
x-axis in the complex plane
Real Numbers

33. To simplify the square root of a negative number
has a solution.
Complex Multiplication
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Real Numbers

34. For real a and b - a + bi =
0 if and only if a = b = 0
Polar Coordinates - z
i^4
Real and Imaginary Parts

35. The modulus of the complex number z= a + ib now can be interpreted as
i^0
Imaginary Numbers
i^1
the distance from z to the origin in the complex plane

36. Has exactly n roots by the fundamental theorem of algebra
Polar Coordinates - z
Any polynomial O(xn) - (n > 0)
sin iy
i^2

37. Any number not rational
natural
Polar Coordinates - r
irrational
z1 ^ (z2)

38. ½(e^(-y) +e^(y)) = cosh y
the distance from z to the origin in the complex plane
Complex numbers are points in the plane
sin iy
cos iy

39. 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
point of inflection
Roots of Unity
natural
adding complex numbers

40. I
irrational
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
The Complex Numbers
i^1

41. Root negative - has letter i
For real a and b - a + bi = 0 if and only if a = b = 0
imaginary
z - z*
Polar Coordinates - cos?

42. 2nd. Rule of Complex Arithmetic

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

43. 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
Polar Coordinates - z
Complex Exponentiation
i^4
the complex numbers

44. The complex number z representing a+bi.
How to find any Power
Real Numbers
cosh²y - sinh²y
Affix

45. A complex number may be taken to the power of another complex number.
Complex Exponentiation
i^3
-1
Polar Coordinates - z

46. x + iy = r(cos? + isin?) = re^(i?)
Polar Coordinates - z
i²
radicals
Euler Formula

47. When two complex numbers are added together.
Complex Addition
Imaginary number
sin iy
real

48. Real and imaginary numbers
i²
z - z*
cos iy
complex numbers

49. Derives z = a+bi
Euler Formula
Polar Coordinates - Multiplication by i
imaginary
Integers

50. A number that cannot be expressed as a fraction for any integer.
(cos? +isin?)n
'i'
conjugate
Irrational 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