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. 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
Polar Coordinates - z
complex
Real and Imaginary Parts
non-integers

2. Root negative - has letter i
Absolute Value of a Complex Number
imaginary
sin z
|z-w|

3. 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
a real number: (a + bi)(a - bi) = a² + b²
adding complex numbers
transcendental
How to solve (2i+3)/(9-i)

4. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Absolute Value of a Complex Number
multiply the numerator and the denominator by the complex conjugate of the denominator.
Polar Coordinates - r
Polar Coordinates - cos?

5. 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
Any polynomial O(xn) - (n > 0)
Rules of Complex Arithmetic
i^2
Imaginary Unit

6. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8
How to multiply complex nubers(2+i)(2i-3)
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Complex Numbers: Add & subtract
Polar Coordinates - Multiplication by i

7. When two complex numbers are added together.
z - z*
Complex Addition
Real Numbers
imaginary

8. E^(ln r) e^(i?) e^(2pin)
How to solve (2i+3)/(9-i)
complex
point of inflection
e^(ln z)

9. A² + b² - real and non negative
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Rules of Complex Arithmetic
Every complex number has the 'Standard Form': a + bi for some real a and b.
zz*

10. y / r
e^(ln z)
-1
We say that c+di and c-di are complex conjugates.
Polar Coordinates - sin?

11. 3rd. Rule of Complex Arithmetic
Absolute Value of a Complex Number
Polar Coordinates - Arg(z*)
For real a and b - a + bi = 0 if and only if a = b = 0
can't get out of the complex numbers by adding (or subtracting) or multiplying two

12. A plot of complex numbers as points.
transcendental
imaginary
Argand diagram
Irrational Number

13. R?¹(cos? - isin?)
Euler Formula
Polar Coordinates - z?¹
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
subtracting complex numbers

14. ½(e^(iz) + e^(-iz))
natural
adding complex numbers
cos z
Polar Coordinates - Arg(z*)

15. Cos n? + i sin n? (for all n integers)
We say that c+di and c-di are complex conjugates.
Polar Coordinates - sin?
rational
(cos? +isin?)n

16. 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

17. A+bi
multiply the numerator and the denominator by the complex conjugate of the denominator.
Real Numbers
interchangeable
Complex Number Formula

18. The field of all rational and irrational numbers.
zz*
adding complex numbers
Real Numbers
v(-1)

19. 1
e^(ln z)
i^4
the distance from z to the origin in the complex plane
Polar Coordinates - r

20. 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 Number Formula
Complex Subtraction
Integers
Complex numbers are points in the plane

21. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
Complex Numbers: Multiply
conjugate pairs
Imaginary Numbers
Integers

22. A number that can be expressed as a fraction p/q where q is not equal to 0.
Rational Number
Real Numbers
Polar Coordinates - Arg(z*)
subtracting complex numbers

23. 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

24. 4th. Rule of Complex Arithmetic
Complex Subtraction
|z-w|
imaginary
(a + bi) = (c + bi) = (a + c) + ( b + d)i

25. For real a and b - a + bi =
Absolute Value of a Complex Number
the distance from z to the origin in the complex plane
0 if and only if a = b = 0
non-integers

26. Starts at 1 - does not include 0
adding complex numbers
natural
Imaginary Numbers
Complex Number

27. E ^ (z2 ln z1)
Complex Exponentiation
Polar Coordinates - Arg(z*)
z1 ^ (z2)
point of inflection

28. The reals are just the
rational
multiply the numerator and the denominator by the complex conjugate of the denominator.
a real number: (a + bi)(a - bi) = a² + b²
x-axis in the complex plane

29. Multiply moduli and add arguments
irrational
i^0
i^2 = -1
Polar Coordinates - Multiplication

30. (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
The Complex Numbers
Liouville's Theorem -
How to solve (2i+3)/(9-i)
a real number: (a + bi)(a - bi) = a² + b²

31. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
Complex Number Formula
Complex Subtraction
multiplying complex numbers
i^2

32. 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
Euler's Formula
Euler Formula
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
subtracting complex numbers

33. 1
a real number: (a + bi)(a - bi) = a² + b²
i^2
Imaginary Unit
conjugate pairs

34. In this amazing number field every algebraic equation in z with complex coefficients
four different numbers: i - -i - 1 - and -1.
complex
has a solution.
For real a and b - a + bi = 0 if and only if a = b = 0

35. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.
sin z
adding complex numbers
Complex Numbers: Multiply
Rational Number

36. 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
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
-1
We say that c+di and c-di are complex conjugates.
i^1

37. (a + bi) = (c + bi) =
Rational Number
the distance from z to the origin in the complex plane
(a + c) + ( b + d)i
Imaginary number

38. 1st. Rule of Complex Arithmetic
standard form of complex numbers
i^2 = -1
Field
How to find any Power

39. x + iy = r(cos? + isin?) = re^(i?)
Field
For real a and b - a + bi = 0 if and only if a = b = 0
Polar Coordinates - z
sin z

40. x / r
We say that c+di and c-di are complex conjugates.
Polar Coordinates - cos?
irrational
conjugate pairs

41. R^2 = x
Complex Addition
Polar Coordinates - Arg(z*)
complex
Square Root

42. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
non-integers
rational
conjugate pairs
ln z

43. Derives z = a+bi
z - z*
Euler Formula
z1 / z2
Polar Coordinates - z

44. The square root of -1.
(cos? +isin?)n
Rules of Complex Arithmetic
Complex Numbers: Multiply
Imaginary Unit

45. To simplify a complex fraction
|z-w|
complex
multiply the numerator and the denominator by the complex conjugate of the denominator.
Complex Number

46. 2nd. Rule of Complex Arithmetic

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

47. 1
Rational Number
point of inflection
cosh²y - sinh²y
Imaginary number

48. ? = -tan?
Complex Number
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Polar Coordinates - Arg(z*)
How to add and subtract complex numbers (2-3i)-(4+6i)

49. 2a
z + z*
'i'
cos iy
v(-1)

50. Like pi
(a + bi) = (c + bi) = (a + c) + ( b + d)i
e^(ln z)
Complex numbers are points in the plane
transcendental

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