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. A + bi
Imaginary Numbers
standard form of complex numbers
-1
Complex numbers are points in the plane

2. V(x² + y²) = |z|
the complex numbers
Complex Number
Polar Coordinates - r
standard form of complex numbers

3. A subset within a field.
cos iy
a + bi for some real a and b.
Subfield
i²

4. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
Complex Number Formula
Complex Exponentiation
the complex numbers
How to add and subtract complex numbers (2-3i)-(4+6i)

5. Starts at 1 - does not include 0
subtracting complex numbers
Affix
natural
conjugate pairs

6. (e^(iz) - e^(-iz)) / 2i
sin z
Imaginary number
z1 / z2
Euler Formula

7. 3rd. Rule of Complex Arithmetic
z1 / z2
The Complex Numbers
For real a and b - a + bi = 0 if and only if a = b = 0
Real and Imaginary Parts

8. I
point of inflection
v(-1)
Real Numbers
How to multiply complex nubers(2+i)(2i-3)

9. When two complex numbers are multipiled together.
Complex Multiplication
has a solution.
i²
four different numbers: i - -i - 1 - and -1.

10. Cos n? + i sin n? (for all n integers)
irrational
(cos? +isin?)n
How to find any Power
standard form of complex numbers

11. 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
We say that c+di and c-di are complex conjugates.
Euler's Formula
adding complex numbers
The Complex Numbers

12. z1z2* / |z2|²
Field
Irrational Number
z1 / z2
Roots of Unity

13. 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
Polar Coordinates - Arg(z*)
irrational
the distance from z to the origin in the complex plane

14. ½(e^(-y) +e^(y)) = cosh y
complex
How to multiply complex nubers(2+i)(2i-3)
cos iy
i^2 = -1

15. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
Polar Coordinates - z?¹
How to add and subtract complex numbers (2-3i)-(4+6i)
Euler's Formula
multiplying complex numbers

16. (a + bi)(c + bi) =
Complex Division
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
ln z
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

17. Imaginary number

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

18. 1
i^2
the distance from z to the origin in the complex plane
Complex Multiplication
has a solution.

19. R^2 = x
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Square Root
Real and Imaginary Parts
multiplying complex numbers

20. I^26/4= i^24 x i^2 =-1 so u divide the number by 4 and whatevers left over is the number that its equal to.
|z-w|
How to find any Power
can't get out of the complex numbers by adding (or subtracting) or multiplying two
i^2 = -1

21. Has exactly n roots by the fundamental theorem of algebra
Any polynomial O(xn) - (n > 0)
i^3
x-axis in the complex plane
can't get out of the complex numbers by adding (or subtracting) or multiplying two

22. 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
x-axis in the complex plane
Imaginary Numbers
the complex numbers
Any polynomial O(xn) - (n > 0)

23. 2ib
complex
non-integers
z - z*
Liouville's Theorem -

24. 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

25. Given (4-2i) the complex conjugate would be (4+2i)
Complex Conjugate
How to multiply complex nubers(2+i)(2i-3)
complex numbers
Euler Formula

26. 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.
four different numbers: i - -i - 1 - and -1.
Complex Number Formula
Complex numbers are points in the plane
sin z

27. Like pi
Polar Coordinates - cos?
Complex Exponentiation
transcendental
Rules of Complex Arithmetic

28. A number that cannot be expressed as a fraction for any integer.
Irrational Number
complex numbers
We say that c+di and c-di are complex conjugates.
ln z

29. Divide moduli and subtract arguments
z1 ^ (z2)
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Polar Coordinates - Division
Square Root

30. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
i^3
e^(ln z)
conjugate
complex

31. 1
i^0
rational
Polar Coordinates - r
Complex Addition

32. Any number not rational
irrational
Complex Subtraction
point of inflection
z + z*

33. ? = -tan?
Imaginary number
Roots of Unity
Absolute Value of a Complex Number
Polar Coordinates - Arg(z*)

34. x + iy = r(cos? + isin?) = re^(i?)
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
z - z*
Complex Numbers: Add & subtract
Polar Coordinates - z

35. The reals are just the
-1
How to find any Power
Square Root
x-axis in the complex plane

36. 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

37. (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
i²
How to solve (2i+3)/(9-i)
conjugate pairs
real

38. Rotates anticlockwise by p/2
Irrational Number
Complex numbers are points in the plane
Polar Coordinates - Multiplication by i
conjugate pairs

39. (a + bi) = (c + bi) =
z1 ^ (z2)
(a + c) + ( b + d)i
Argand diagram
natural

40. In this amazing number field every algebraic equation in z with complex coefficients
(a + c) + ( b + d)i
has a solution.
imaginary
Euler Formula

41. A plot of complex numbers as points.
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
'i'
Argand diagram
z - z*

42. 5th. Rule of Complex Arithmetic
irrational
conjugate
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
De Moivre's Theorem

43. ½(e^(iz) + e^(-iz))
|z-w|
cos z
Complex Conjugate
four different numbers: i - -i - 1 - and -1.

44. 1
interchangeable
a real number: (a + bi)(a - bi) = a² + b²
Liouville's Theorem -
i²

45. Not on the numberline
non-integers
Complex Addition
interchangeable
ln z

46. The complex number z representing a+bi.
cos iy
the complex numbers
Imaginary Numbers
Affix

47. We can also think of the point z= a+ ib as
rational
complex
How to add and subtract complex numbers (2-3i)-(4+6i)
the vector (a -b)

48. Root negative - has letter i
a real number: (a + bi)(a - bi) = a² + b²
imaginary
sin iy
z - z*

49. Numbers on a numberline
Complex Subtraction
integers
(a + c) + ( b + d)i
Polar Coordinates - Multiplication by i

50. Where the curvature of the graph changes
irrational
cos z
point of inflection
Complex Numbers: Multiply