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. 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
radicals
Polar Coordinates - sin?
Polar Coordinates - Division
Rules of Complex Arithmetic

2. We can also think of the point z= a+ ib as
adding complex numbers
z1 ^ (z2)
a real number: (a + bi)(a - bi) = a² + b²
the vector (a -b)

3. Real and imaginary numbers
complex numbers
Complex Numbers: Add & subtract
'i'
|z-w|

4. 3rd. Rule of Complex Arithmetic
irrational
For real a and b - a + bi = 0 if and only if a = b = 0
De Moivre's Theorem
i^3

5. When two complex numbers are multipiled together.
Polar Coordinates - r
Complex Multiplication
i^2 = -1
0 if and only if a = b = 0

6. A number that cannot be expressed as a fraction for any integer.
Irrational Number
imaginary
i^3
De Moivre's Theorem

7. Numbers on a numberline
Real Numbers
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
integers
i^4

8. Where the curvature of the graph changes
transcendental
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
point of inflection
Polar Coordinates - r

9. 3
i^3
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - sin?
Any polynomial O(xn) - (n > 0)

10. Multiply moduli and add arguments
Complex Multiplication
Subfield
Polar Coordinates - Multiplication
Roots of Unity

11. A + bi
four different numbers: i - -i - 1 - and -1.
interchangeable
i^2
standard form of complex numbers

12. Starts at 1 - does not include 0
irrational
four different numbers: i - -i - 1 - and -1.
natural
zz*

13. (a + bi)(c + bi) =
How to solve (2i+3)/(9-i)
Roots of Unity
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
i^2

14. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
Rational Number
Complex Numbers: Add & subtract
How to add and subtract complex numbers (2-3i)-(4+6i)
For real a and b - a + bi = 0 if and only if a = b = 0

15. E^(ln r) e^(i?) e^(2pin)
complex
Complex numbers are points in the plane
e^(ln z)
irrational

16. Root negative - has letter i
imaginary
Complex Exponentiation
Complex numbers are points in the plane
Irrational Number

17. (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
Every complex number has the 'Standard Form': a + bi for some real a and b.
non-integers
How to solve (2i+3)/(9-i)
Complex Subtraction

18. Cos n? + i sin n? (for all n integers)
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Liouville's Theorem -
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
(cos? +isin?)n

19. E ^ (z2 ln z1)
Any polynomial O(xn) - (n > 0)
z1 ^ (z2)
Complex Addition
Complex Numbers: Add & subtract

20. ? = -tan?
v(-1)
Imaginary Unit
Polar Coordinates - Arg(z*)
Complex Number

21. 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

22. A complex number and its conjugate
conjugate pairs
Polar Coordinates - z
Liouville's Theorem -
Complex Addition

23. When two complex numbers are added together.
Complex Addition
the distance from z to the origin in the complex plane
Complex Division
zz*

24. 2nd. Rule of Complex Arithmetic

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

25. 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
conjugate
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
subtracting complex numbers
Polar Coordinates - Multiplication

26. 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.
z + z*
Complex Number

27. A complex number may be taken to the power of another complex number.
Complex Exponentiation
standard form of complex numbers
Euler Formula
can't get out of the complex numbers by adding (or subtracting) or multiplying two

28. 1
(a + c) + ( b + d)i
z - z*
i^0
'i'

29. A² + b² - real and non negative
Polar Coordinates - z
Polar Coordinates - r
Argand diagram
zz*

30. Derives z = a+bi
Euler's Formula
Euler Formula
Polar Coordinates - Division
Complex Number

31. When two complex numbers are divided.
Polar Coordinates - sin?
Roots of Unity
Complex Division
adding complex numbers

32. Any number not rational
sin z
a + bi for some real a and b.
irrational
0 if and only if a = b = 0

33. A subset within a field.
i^0
adding complex numbers
Subfield
(a + c) + ( b + d)i

34. 1
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Complex Division
cosh²y - sinh²y
(cos? +isin?)n

35. x + iy = r(cos? + isin?) = re^(i?)
|z-w|
Subfield
imaginary
Polar Coordinates - z

36. Given (4-2i) the complex conjugate would be (4+2i)
Polar Coordinates - r
Complex Conjugate
radicals
Argand diagram

37. When two complex numbers are subtracted from one another.
cos iy
z - z*
Complex Subtraction
'i'

38. 1
How to solve (2i+3)/(9-i)
can't get out of the complex numbers by adding (or subtracting) or multiplying two
i^4
complex

39. 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

40. Like pi
transcendental
the vector (a -b)
Imaginary Unit
rational

41. x / r
|z| = mod(z)
How to add and subtract complex numbers (2-3i)-(4+6i)
Polar Coordinates - cos?
the complex numbers

42. All the powers of i can be written as
Euler's Formula
How to multiply complex nubers(2+i)(2i-3)
Irrational Number
four different numbers: i - -i - 1 - and -1.

43. 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

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
adding complex numbers
zz*
cos iy
the complex numbers

45. 1
Real and Imaginary Parts
complex numbers
natural
i^2

46. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Roots of Unity
Complex Subtraction
the distance from z to the origin in the complex plane
Real Numbers

47. The square root of -1.
standard form of complex numbers
0 if and only if a = b = 0
Imaginary Unit
Euler's Formula

48. xpressions such as ``the complex number z'' - and ``the point z'' are now
Absolute Value of a Complex Number
interchangeable
Affix
radicals

49. The modulus of the complex number z= a + ib now can be interpreted as
the vector (a -b)
the distance from z to the origin in the complex plane
|z-w|
x-axis in the complex plane

50. Written as fractions - terminating + repeating decimals
the distance from z to the origin in the complex plane
rational
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
(a + bi) = (c + bi) = (a + c) + ( b + d)i