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. 5th. Rule of Complex Arithmetic
cosh²y - sinh²y
How to find any Power
the vector (a -b)
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

2. For real a and b - a + bi =
can't get out of the complex numbers by adding (or subtracting) or multiplying two
v(-1)
0 if and only if a = b = 0
Polar Coordinates - Arg(z*)

3. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Roots of Unity
Polar Coordinates - z
Euler Formula
imaginary

4. 1
the distance from z to the origin in the complex plane
point of inflection
Liouville's Theorem -
i²

5. All the powers of i can be written as
How to solve (2i+3)/(9-i)
We say that c+di and c-di are complex conjugates.
four different numbers: i - -i - 1 - and -1.
sin iy

6. 1
(a + c) + ( b + d)i
rational
i^4
cos z

7. I
0 if and only if a = b = 0
Integers
multiply the numerator and the denominator by the complex conjugate of the denominator.
v(-1)

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

9. 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
Complex Multiplication
Complex Conjugate
We say that c+di and c-di are complex conjugates.
z - z*

10. The square root of -1.
i^2 = -1
Imaginary Unit
Rules of Complex Arithmetic
Affix

11. We see in this way that the distance between two points z and w in the complex plane is
|z-w|
conjugate pairs
Imaginary Unit
Subfield

12. The reals are just the
real
x-axis in the complex plane
a real number: (a + bi)(a - bi) = a² + b²
Rules of Complex Arithmetic

13. ? = -tan?
Polar Coordinates - Arg(z*)
adding complex numbers
We say that c+di and c-di are complex conjugates.
Field

14. 1
Square Root
cosh²y - sinh²y
standard form of complex numbers
x-axis in the complex plane

15. When two complex numbers are divided.
Field
four different numbers: i - -i - 1 - and -1.
Complex Division
zz*

16. Real and imaginary numbers
e^(ln z)
Real Numbers
(a + bi) = (c + bi) = (a + c) + ( b + d)i
complex numbers

17. Multiply moduli and add arguments
How to solve (2i+3)/(9-i)
-1
Polar Coordinates - Multiplication
Polar Coordinates - Arg(z*)

18. Rotates anticlockwise by p/2
Complex Multiplication
-1
imaginary
Polar Coordinates - Multiplication by i

19. 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
Real and Imaginary Parts
interchangeable
radicals
Complex Numbers: Multiply

20. Not on the numberline
irrational
subtracting complex numbers
non-integers
i²

21. (a + bi) = (c + bi) =
(a + c) + ( b + d)i
zz*
v(-1)
Complex Number Formula

22. y / r
Polar Coordinates - sin?
Integers
Complex Addition
e^(ln z)

23. ½(e^(iz) + e^(-iz))
Liouville's Theorem -
cos z
adding complex numbers
Absolute Value of a Complex Number

24. Numbers on a numberline
integers
four different numbers: i - -i - 1 - and -1.
Complex Division
Complex Numbers: Multiply

25. A+bi
Complex Number Formula
subtracting complex numbers
For real a and b - a + bi = 0 if and only if a = b = 0
Polar Coordinates - r

26. In this amazing number field every algebraic equation in z with complex coefficients
has a solution.
Irrational Number
'i'
z1 ^ (z2)

27. Have radical
Polar Coordinates - sin?
radicals
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - Multiplication

28. 3
Polar Coordinates - r
i^3
interchangeable
De Moivre's Theorem

29. Derives z = a+bi
The Complex Numbers
Euler Formula
standard form of complex numbers
Field

30. All numbers
complex
Complex Multiplication
natural
De Moivre's Theorem

31. 2a
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Imaginary Numbers
z + z*
Complex numbers are points in the plane

32. 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
cos z
Complex Division
Complex Numbers: Add & subtract
point of inflection

33. Equivalent to an Imaginary Unit.
|z| = mod(z)
Imaginary number
subtracting complex numbers
z - z*

34. I
How to add and subtract complex numbers (2-3i)-(4+6i)
real
i^2
i^1

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.
De Moivre's Theorem
Complex numbers are points in the plane
Complex Numbers: Multiply
complex

36. x + iy = r(cos? + isin?) = re^(i?)
Polar Coordinates - z
How to find any Power
We say that c+di and c-di are complex conjugates.
Complex Exponentiation

37. The field of all rational and irrational numbers.
Real Numbers
i^1
Polar Coordinates - Multiplication
Complex numbers are points in the plane

38. R^2 = x
natural
Imaginary Numbers
non-integers
Square Root

39. When two complex numbers are added together.
Complex Addition
non-integers
radicals
the distance from z to the origin in the complex plane

40. Divide moduli and subtract arguments
non-integers
Polar Coordinates - Division
Polar Coordinates - z
Complex Division

41. Starts at 1 - does not include 0
natural
(a + c) + ( b + d)i
four different numbers: i - -i - 1 - and -1.
We say that c+di and c-di are complex conjugates.

42. 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
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
|z-w|
subtracting complex numbers
'i'

43. I = imaginary unit - i² = -1 or i = v-1
Euler Formula
Complex Exponentiation
i^3
Imaginary Numbers

44. 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.'
Complex Number
multiply the numerator and the denominator by the complex conjugate of the denominator.
'i'
a real number: (a + bi)(a - bi) = a² + b²

45. A + bi
zz*
How to add and subtract complex numbers (2-3i)-(4+6i)
standard form of complex numbers
the complex numbers

46. A subset within a field.
Imaginary number
Subfield
i^0
Euler Formula

47. The product of an imaginary number and its conjugate is
Complex Subtraction
a real number: (a + bi)(a - bi) = a² + b²
Roots of Unity
Any polynomial O(xn) - (n > 0)

48. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
Integers
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
zz*
'i'

49. To simplify a complex fraction
Rational Number
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Complex Addition
multiply the numerator and the denominator by the complex conjugate of the denominator.

50. Given (4-2i) the complex conjugate would be (4+2i)
conjugate pairs
How to add and subtract complex numbers (2-3i)-(4+6i)
Complex numbers are points in the plane
Complex Conjugate