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. No i
real
zz*
De Moivre's Theorem
i²

2. Where the curvature of the graph changes
ln z
Liouville's Theorem -
point of inflection
Polar Coordinates - r

3. x / r
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
z1 / z2
Polar Coordinates - cos?
Field

4. Divide moduli and subtract arguments
Any polynomial O(xn) - (n > 0)
Polar Coordinates - Division
the complex numbers
Complex Division

5. All numbers
Euler Formula
Affix
subtracting complex numbers
complex

6. Derives z = a+bi
Any polynomial O(xn) - (n > 0)
i^1
natural
Euler Formula

7. 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.'
Polar Coordinates - r
z - z*
Complex Number
(a + bi) = (c + bi) = (a + c) + ( b + d)i

8. Like pi
Real and Imaginary Parts
transcendental
Complex Number
x-axis in the complex plane

9. 1
cosh²y - sinh²y
Square Root
ln z
z - z*

10. For real a and b - a + bi =
0 if and only if a = b = 0
'i'
Rational Number
four different numbers: i - -i - 1 - and -1.

11. z1z2* / |z2|²
Subfield
z1 / z2
Roots of Unity
Polar Coordinates - r

12. To simplify the square root of a negative number
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Irrational Number
Polar Coordinates - z
non-integers

13. Has exactly n roots by the fundamental theorem of algebra
Any polynomial O(xn) - (n > 0)
Polar Coordinates - Multiplication by i
Imaginary number
i^1

14. ½(e^(-y) +e^(y)) = cosh y
cos iy
subtracting complex numbers
rational
i²

15. I
irrational
i^1
We say that c+di and c-di are complex conjugates.
the complex numbers

16. I = imaginary unit - i² = -1 or i = v-1
Imaginary Numbers
Real Numbers
Complex Number
Polar Coordinates - cos?

17. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
Complex Multiplication
radicals
How to add and subtract complex numbers (2-3i)-(4+6i)
Integers

18. Given (4-2i) the complex conjugate would be (4+2i)
Square Root
Complex Conjugate
conjugate pairs
imaginary

19. (a + bi)(c + bi) =
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
sin z
z - z*
Real and Imaginary Parts

20. 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.
Complex Numbers: Multiply
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
|z| = mod(z)
complex numbers

21. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Complex Conjugate
The Complex Numbers
Subfield
Absolute Value of a Complex Number

22. (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
How to solve (2i+3)/(9-i)
z - z*
i^3
non-integers

23. Multiply moduli and add arguments
subtracting complex numbers
Polar Coordinates - z?¹
i^2 = -1
Polar Coordinates - Multiplication

24. A² + b² - real and non negative
Integers
zz*
z - z*
Every complex number has the 'Standard Form': a + bi for some real a and b.

25. Equivalent to an Imaginary Unit.
the vector (a -b)
Imaginary number
-1
Roots of Unity

26. When two complex numbers are multipiled together.
natural
Complex Multiplication
Subfield
standard form of complex numbers

27. A complex number and its conjugate
Polar Coordinates - Division
conjugate pairs
How to find any Power
conjugate

28. Have radical
De Moivre's Theorem
radicals
standard form of complex numbers
a + bi for some real a and b.

29. 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

30. (e^(-y) - e^(y)) / 2i = i sinh y
e^(ln z)
sin iy
'i'
Complex Number

31. 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
transcendental
Polar Coordinates - cos?
adding complex numbers
We say that c+di and c-di are complex conjugates.

32. A plot of complex numbers as points.
Argand diagram
i^4
rational
Imaginary Unit

33. Numbers on a numberline
irrational
Polar Coordinates - Arg(z*)
integers
Roots of Unity

34. The square root of -1.
Polar Coordinates - cos?
Real Numbers
For real a and b - a + bi = 0 if and only if a = b = 0
Imaginary Unit

35. 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

36. 5th. Rule of Complex Arithmetic
Complex Number Formula
The Complex Numbers
Imaginary Numbers
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

37. I^2 =
Polar Coordinates - cos?
-1
Polar Coordinates - Arg(z*)
Complex Numbers: Add & subtract

38. R?¹(cos? - isin?)
Any polynomial O(xn) - (n > 0)
Polar Coordinates - z?¹
i^0
0 if and only if a = b = 0

39. We see in this way that the distance between two points z and w in the complex plane is
Complex Numbers: Add & subtract
|z-w|
Subfield
natural

40. 2a
z + z*
Euler Formula
i^0
Square Root

41. Starts at 1 - does not include 0
conjugate pairs
the complex numbers
adding complex numbers
natural

42. Cos n? + i sin n? (for all n integers)
(cos? +isin?)n
Complex Multiplication
the vector (a -b)
Complex Numbers: Multiply

43. V(x² + y²) = |z|
Roots of Unity
Polar Coordinates - r
Complex Subtraction
Irrational Number

44. 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
the complex numbers
For real a and b - a + bi = 0 if and only if a = b = 0
x-axis in the complex plane
(a + bi) = (c + bi) = (a + c) + ( b + d)i

45. 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
cosh²y - sinh²y
Rules of Complex Arithmetic
x-axis in the complex plane
a + bi for some real a and b.

46. To simplify a complex fraction
imaginary
Complex Exponentiation
multiply the numerator and the denominator by the complex conjugate of the denominator.
multiplying complex numbers

47. We can also think of the point z= a+ ib as
Every complex number has the 'Standard Form': a + bi for some real a and b.
Field
The Complex Numbers
the vector (a -b)

48. The field of all rational and irrational numbers.
conjugate pairs
|z-w|
transcendental
Real Numbers

49. The complex number z representing a+bi.
i^3
a + bi for some real a and b.
Affix
complex numbers

50. Not on the numberline
cos z
Real Numbers
non-integers
v(-1)

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