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. R^2 = x
x-axis in the complex plane
Square Root
|z| = mod(z)
Polar Coordinates - Division

2. A² + b² - real and non negative
cos iy
We say that c+di and c-di are complex conjugates.
the distance from z to the origin in the complex plane
zz*

3. The reals are just the
a real number: (a + bi)(a - bi) = a² + b²
Polar Coordinates - z?¹
irrational
x-axis in the complex plane

4. I
Complex Conjugate
'i'
i^1
Integers

5. 4th. Rule of Complex Arithmetic
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Complex Exponentiation
Real and Imaginary Parts
cos iy

6. ? = -tan?
z1 / z2
z + z*
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - Arg(z*)

7. (e^(-y) - e^(y)) / 2i = i sinh y
How to solve (2i+3)/(9-i)
We say that c+di and c-di are complex conjugates.
sin iy
Liouville's Theorem -

8. 3rd. Rule of Complex Arithmetic
a + bi for some real a and b.
For real a and b - a + bi = 0 if and only if a = b = 0
Any polynomial O(xn) - (n > 0)
z - z*

9. For real a and b - a + bi =
zz*
0 if and only if a = b = 0
Irrational Number
interchangeable

10. Given (4-2i) the complex conjugate would be (4+2i)
Complex Number
complex
i^1
Complex Conjugate

11. 2nd. Rule of Complex Arithmetic

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

12. 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
'i'
Affix
z + z*

13. A number that cannot be expressed as a fraction for any integer.
subtracting complex numbers
Real Numbers
e^(ln z)
Irrational Number

14. 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
Irrational Number
i^2
The Complex Numbers
adding complex numbers

15. E ^ (z2 ln z1)
z1 ^ (z2)
adding complex numbers
For real a and b - a + bi = 0 if and only if a = b = 0
interchangeable

16. 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
Rational Number
standard form of complex numbers
We say that c+di and c-di are complex conjugates.
Polar Coordinates - sin?

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. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
ln z
z - z*
Absolute Value of a Complex Number
complex

19. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
Polar Coordinates - cos?
i^0
|z-w|
conjugate

20. 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
Complex Numbers: Add & subtract
We say that c+di and c-di are complex conjugates.
real
Absolute Value of a Complex Number

21. z1z2* / |z2|²
standard form of complex numbers
z1 / z2
Complex Numbers: Add & subtract
point of inflection

22. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called
conjugate pairs
The Complex Numbers
rational
non-integers

23. To simplify the square root of a negative number
adding complex numbers
0 if and only if a = b = 0
How to solve (2i+3)/(9-i)
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

24. (e^(iz) - e^(-iz)) / 2i
sin z
Imaginary number
Imaginary Numbers
e^(ln z)

25. 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 Conjugate
Complex Number
z1 ^ (z2)
How to solve (2i+3)/(9-i)

26. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
Euler Formula
|z-w|
Field
Affix

27. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Liouville's Theorem -
zz*
Absolute Value of a Complex Number
sin iy

28. I
Polar Coordinates - Division
conjugate pairs
Polar Coordinates - Arg(z*)
v(-1)

29. A + bi
Imaginary Numbers
standard form of complex numbers
point of inflection
imaginary

30. No i
real
Complex Number Formula
rational
subtracting complex numbers

31. E^(ln r) e^(i?) e^(2pin)
Field
Euler Formula
e^(ln z)
real

32. The field of all rational and irrational numbers.
Imaginary Numbers
For real a and b - a + bi = 0 if and only if a = b = 0
Real Numbers
a real number: (a + bi)(a - bi) = a² + b²

33. I = imaginary unit - i² = -1 or i = v-1
subtracting complex numbers
Affix
Imaginary Numbers
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

34. Starts at 1 - does not include 0
natural
Complex Division
Polar Coordinates - Division
cos z

35. Root negative - has letter i
imaginary
-1
Polar Coordinates - Multiplication
multiply the numerator and the denominator by the complex conjugate of the denominator.

36. Multiply moduli and add arguments
Polar Coordinates - Multiplication
can't get out of the complex numbers by adding (or subtracting) or multiplying two
i^1
e^(ln z)

37. Have radical
radicals
multiplying complex numbers
-1
adding complex numbers

38. A complex number and its conjugate
conjugate pairs
ln z
i^0
Complex Number Formula

39. 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

40. Any number not rational
subtracting complex numbers
Affix
irrational
Roots of Unity

41. 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
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Numbers: Multiply
the complex numbers
zz*

42. Cos n? + i sin n? (for all n integers)
(cos? +isin?)n
conjugate pairs
Complex Exponentiation
Rules of Complex Arithmetic

43. 1st. Rule of Complex Arithmetic
i^2 = -1
Square Root
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Imaginary number

44. y / r
Polar Coordinates - z?¹
Rules of Complex Arithmetic
i^0
Polar Coordinates - sin?

45. 2a
(cos? +isin?)n
complex
Integers
z + z*

46. Written as fractions - terminating + repeating decimals
the distance from z to the origin in the complex plane
Polar Coordinates - Multiplication by i
Any polynomial O(xn) - (n > 0)
rational

47. R?¹(cos? - isin?)
Polar Coordinates - r
conjugate pairs
How to add and subtract complex numbers (2-3i)-(4+6i)
Polar Coordinates - z?¹

48. A complex number may be taken to the power of another complex number.
Complex Number Formula
Complex Exponentiation
|z-w|
Argand diagram

49. 1
imaginary
a + bi for some real a and b.
Subfield
i^0

50. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
Liouville's Theorem -
Polar Coordinates - cos?
transcendental
How to add and subtract complex numbers (2-3i)-(4+6i)

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