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. 3rd. Rule of Complex Arithmetic
Complex Division
Euler's Formula
How to solve (2i+3)/(9-i)
For real a and b - a + bi = 0 if and only if a = b = 0

2. I
Imaginary Unit
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Subfield
i^1

3. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
multiplying complex numbers
Field
For real a and b - a + bi = 0 if and only if a = b = 0
How to find any Power

4. 1
i^4
Complex numbers are points in the plane
e^(ln z)
Polar Coordinates - Multiplication

5. Not on the numberline
Rules of Complex Arithmetic
non-integers
i^2 = -1
Polar Coordinates - r

6. Real and imaginary numbers
conjugate pairs
complex numbers
Liouville's Theorem -
subtracting complex numbers

7. 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)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - Arg(z*)
Real and Imaginary Parts
Any polynomial O(xn) - (n > 0)

8. (a + bi) = (c + bi) =
conjugate pairs
0 if and only if a = b = 0
Argand diagram
(a + c) + ( b + d)i

9. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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

10. Written as fractions - terminating + repeating decimals
Euler Formula
point of inflection
rational
Any polynomial O(xn) - (n > 0)

11. Derives z = a+bi
Euler Formula
cos iy
How to multiply complex nubers(2+i)(2i-3)
x-axis in the complex plane

12. I = imaginary unit - i² = -1 or i = v-1
Rules of Complex Arithmetic
Polar Coordinates - z
integers
Imaginary Numbers

13. Multiply moduli and add arguments
a + bi for some real a and b.
standard form of complex numbers
Euler Formula
Polar Coordinates - Multiplication

14. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
point of inflection
cosh²y - sinh²y
De Moivre's Theorem
Integers

15. A plot of complex numbers as points.
Argand diagram
Field
sin iy
Any polynomial O(xn) - (n > 0)

16. 1
Complex Numbers: Multiply
Euler Formula
v(-1)
cosh²y - sinh²y

17. 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

18. Has exactly n roots by the fundamental theorem of algebra
Any polynomial O(xn) - (n > 0)
i^1
0 if and only if a = b = 0
Complex Numbers: Multiply

19. ½(e^(iz) + e^(-iz))
Complex numbers are points in the plane
cos z
standard form of complex numbers
point of inflection

20. Cos n? + i sin n? (for all n integers)
radicals
(cos? +isin?)n
Square Root
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

21. A + bi
standard form of complex numbers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Subfield
Complex Multiplication

22. 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.
sin z
a + bi for some real a and b.
Complex numbers are points in the plane
|z| = mod(z)

23. ? = -tan?
i^4
Polar Coordinates - Arg(z*)
i^3
Complex Number Formula

24. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
Euler Formula
ln z
subtracting complex numbers
i²

25. Have radical
conjugate pairs
radicals
i^2
rational

26. V(x² + y²) = |z|
subtracting complex numbers
a + bi for some real a and b.
How to multiply complex nubers(2+i)(2i-3)
Polar Coordinates - r

27. 1
|z| = mod(z)
Polar Coordinates - sin?
interchangeable
i²

28. A complex number may be taken to the power of another complex number.
0 if and only if a = b = 0
imaginary
Complex Exponentiation
Any polynomial O(xn) - (n > 0)

29. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
Affix
multiplying complex numbers
the vector (a -b)
i^2

30. 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
cos iy
a + bi for some real a and b.
Polar Coordinates - r
the complex numbers

31. E ^ (z2 ln z1)
e^(ln z)
z1 ^ (z2)
Polar Coordinates - z?¹
i^2

32. 5th. Rule of Complex Arithmetic
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
ln z
|z| = mod(z)
Polar Coordinates - r

33. 4th. Rule of Complex Arithmetic
standard form of complex numbers
Polar Coordinates - z?¹
How to solve (2i+3)/(9-i)
(a + bi) = (c + bi) = (a + c) + ( b + d)i

34. For real a and b - a + bi =
a real number: (a + bi)(a - bi) = a² + b²
0 if and only if a = b = 0
(cos? +isin?)n
complex

35. A+bi
cosh²y - sinh²y
Complex Number Formula
Polar Coordinates - Multiplication by i
natural

36. A number that can be expressed as a fraction p/q where q is not equal to 0.
Rational Number
De Moivre's Theorem
integers
Every complex number has the 'Standard Form': a + bi for some real a and b.

37. The field of all rational and irrational numbers.
Rules of Complex Arithmetic
Subfield
How to add and subtract complex numbers (2-3i)-(4+6i)
Real Numbers

38. 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.'
conjugate pairs
Imaginary Numbers
point of inflection
Complex Number

39. R?¹(cos? - isin?)
Irrational Number
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
subtracting complex numbers
Polar Coordinates - z?¹

40. 1st. Rule of Complex Arithmetic
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
i^2 = -1
Polar Coordinates - z?¹
Polar Coordinates - Arg(z*)

41. 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
zz*
Rules of Complex Arithmetic
Liouville's Theorem -
transcendental

42. All the powers of i can be written as
four different numbers: i - -i - 1 - and -1.
the complex numbers
Subfield
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

43. The product of an imaginary number and its conjugate is
the complex numbers
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
multiply the numerator and the denominator by the complex conjugate of the denominator.
a real number: (a + bi)(a - bi) = a² + b²

44. A² + b² - real and non negative
complex numbers
Polar Coordinates - z
zz*
z - z*

45. (a + bi)(c + bi) =
i^2
a + bi for some real a and b.
Polar Coordinates - Division
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

46. (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)
The Complex Numbers
Complex Number
standard form of complex numbers

47. 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
a + bi for some real a and b.
We say that c+di and c-di are complex conjugates.
Subfield

48. All numbers
the distance from z to the origin in the complex plane
multiply the numerator and the denominator by the complex conjugate of the denominator.
complex
Every complex number has the 'Standard Form': a + bi for some real a and b.

49. Rotates anticlockwise by p/2
Absolute Value of a Complex Number
Complex Division
Polar Coordinates - Multiplication by i
0 if and only if a = b = 0

50. To simplify a complex fraction
imaginary
multiply the numerator and the denominator by the complex conjugate of the denominator.
has a solution.
cosh²y - sinh²y

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