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. Multiply moduli and add arguments
conjugate
Polar Coordinates - Multiplication
(a + bi) = (c + bi) = (a + c) + ( b + d)i
rational

2. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
conjugate
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
-1
has a solution.

3. 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
Liouville's Theorem -
the complex numbers
Polar Coordinates - cos?
ln z

4. (a + bi)(c + bi) =
Roots of Unity
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
How to multiply complex nubers(2+i)(2i-3)

5. I = imaginary unit - i² = -1 or i = v-1
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Imaginary Numbers
Square Root
Polar Coordinates - Arg(z*)

6. Any number not rational
cos iy
natural
irrational
Complex Multiplication

7. 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

8. 2nd. Rule of Complex Arithmetic

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

9. Equivalent to an Imaginary Unit.
Polar Coordinates - Multiplication by i
How to add and subtract complex numbers (2-3i)-(4+6i)
standard form of complex numbers
Imaginary number

10. For real a and b - a + bi =
multiplying complex numbers
Euler Formula
e^(ln z)
0 if and only if a = b = 0

11. 1
can't get out of the complex numbers by adding (or subtracting) or multiplying two
cosh²y - sinh²y
multiply the numerator and the denominator by the complex conjugate of the denominator.
Euler's Formula

12. Root negative - has letter i
v(-1)
imaginary
Argand diagram
Square Root

13. In this amazing number field every algebraic equation in z with complex coefficients
has a solution.
How to add and subtract complex numbers (2-3i)-(4+6i)
We say that c+di and c-di are complex conjugates.
Euler Formula

14. The modulus of the complex number z= a + ib now can be interpreted as
the distance from z to the origin in the complex plane
Any polynomial O(xn) - (n > 0)
Rules of Complex Arithmetic
sin iy

15. A+bi
z - z*
subtracting complex numbers
Argand diagram
Complex Number Formula

16. We can also think of the point z= a+ ib as
z - z*
Complex Division
the vector (a -b)
Polar Coordinates - cos?

17. Numbers on a numberline
integers
Real and Imaginary Parts
sin z
irrational

18. z1z2* / |z2|²
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - r
z1 / z2
i^1

19. 2ib
For real a and b - a + bi = 0 if and only if a = b = 0
ln z
z - z*
four different numbers: i - -i - 1 - and -1.

20. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
natural
i^1
Absolute Value of a Complex Number
Real Numbers

21. 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
Integers
Polar Coordinates - Arg(z*)
How to find any Power

22. 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.'
adding complex numbers
i^3
Complex Number
0 if and only if a = b = 0

23. The reals are just the
x-axis in the complex plane
i^3
(a + c) + ( b + d)i
transcendental

24. 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
Any polynomial O(xn) - (n > 0)
radicals
Real and Imaginary Parts
Euler's Formula

25. 1st. Rule of Complex Arithmetic
v(-1)
x-axis in the complex plane
i^2 = -1
Irrational Number

26. E^(ln r) e^(i?) e^(2pin)
e^(ln z)
Liouville's Theorem -
Complex Subtraction
Complex Addition

27. Real and imaginary numbers
complex numbers
four different numbers: i - -i - 1 - and -1.
Imaginary Numbers
integers

28. 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
i^2
-1
Square Root
subtracting complex numbers

29. When two complex numbers are subtracted from one another.
Complex Subtraction
z - z*
For real a and b - a + bi = 0 if and only if a = b = 0
-1

30. To simplify a complex fraction
point of inflection
Rational Number
Polar Coordinates - Division
multiply the numerator and the denominator by the complex conjugate of the denominator.

31. x + iy = r(cos? + isin?) = re^(i?)
Complex Addition
real
Polar Coordinates - z
adding complex numbers

32. Has exactly n roots by the fundamental theorem of algebra
four different numbers: i - -i - 1 - and -1.
Any polynomial O(xn) - (n > 0)
zz*
Roots of Unity

33. Rotates anticlockwise by p/2
Polar Coordinates - Multiplication by i
a real number: (a + bi)(a - bi) = a² + b²
Polar Coordinates - Division
imaginary

34. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
conjugate pairs
i^2 = -1
Field
i^3

35. ½(e^(-y) +e^(y)) = cosh y
radicals
How to solve (2i+3)/(9-i)
cos iy
Complex Multiplication

36. 4th. Rule of Complex Arithmetic
Polar Coordinates - cos?
can't get out of the complex numbers by adding (or subtracting) or multiplying two
(a + bi) = (c + bi) = (a + c) + ( b + d)i
a real number: (a + bi)(a - bi) = a² + b²

37. Imaginary number

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

38. We see in this way that the distance between two points z and w in the complex plane is
Complex Numbers: Add & subtract
z1 / z2
|z-w|
cos iy

39. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
'i'
Complex Addition
i^4
How to add and subtract complex numbers (2-3i)-(4+6i)

40. Cos n? + i sin n? (for all n integers)
v(-1)
(cos? +isin?)n
complex
-1

41. I
Complex Numbers: Multiply
Imaginary Numbers
i^1
Roots of Unity

42. A plot of complex numbers as points.
Argand diagram
(a + bi) = (c + bi) = (a + c) + ( b + d)i
transcendental
Integers

43. V(x² + y²) = |z|
Polar Coordinates - Division
Polar Coordinates - r
zz*
non-integers

44. (e^(-y) - e^(y)) / 2i = i sinh y
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
(a + c) + ( b + d)i
sin iy
subtracting complex numbers

45. A complex number may be taken to the power of another complex number.
Complex Numbers: Add & subtract
multiply the numerator and the denominator by the complex conjugate of the denominator.
Complex Exponentiation
multiplying complex numbers

46. When two complex numbers are divided.
Imaginary Unit
Complex Number
zz*
Complex Division

47. 1
ln z
Complex Subtraction
Complex Division
i^0

48. R^2 = x
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
i²
Affix
Square Root

49. A² + b² - real and non negative
x-axis in the complex plane
sin z
complex
zz*

50. R?¹(cos? - isin?)
i^2 = -1
radicals
interchangeable
Polar Coordinates - z?¹

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

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