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
Rules of Complex Arithmetic
Complex Subtraction
complex
the complex numbers

2. Root negative - has letter i
Liouville's Theorem -
imaginary
transcendental
Imaginary Unit

3. 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
irrational
Euler's Formula
v(-1)

4. y / r
four different numbers: i - -i - 1 - and -1.
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Imaginary Numbers
Polar Coordinates - sin?

5. I
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
v(-1)
Real Numbers
Euler's Formula

6. (a + bi) = (c + bi) =
the complex numbers
-1
Integers
(a + c) + ( b + d)i

7. 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
subtracting complex numbers
imaginary
irrational
x-axis in the complex plane

8. 2ib
Rules of Complex Arithmetic
z1 ^ (z2)
Imaginary number
z - z*

9. Where the curvature of the graph changes
point of inflection
Any polynomial O(xn) - (n > 0)
(a + bi) = (c + bi) = (a + c) + ( b + d)i
complex

10. Rotates anticlockwise by p/2
Polar Coordinates - Multiplication by i
z1 ^ (z2)
For real a and b - a + bi = 0 if and only if a = b = 0
cos iy

11. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
radicals
Any polynomial O(xn) - (n > 0)
Euler's Formula
How to add and subtract complex numbers (2-3i)-(4+6i)

12. A + bi
(a + c) + ( b + d)i
standard form of complex numbers
How to find any Power
The Complex Numbers

13. 1
conjugate pairs
i^0
rational
cos iy

14. R?¹(cos? - isin?)
Polar Coordinates - z?¹
a real number: (a + bi)(a - bi) = a² + b²
i^0
Polar Coordinates - sin?

15. 3
i^3
interchangeable
ln z
For real a and b - a + bi = 0 if and only if a = b = 0

16. V(x² + y²) = |z|
Polar Coordinates - r
Complex numbers are points in the plane
x-axis in the complex plane
Rules of Complex Arithmetic

17. Starts at 1 - does not include 0
sin iy
natural
the distance from z to the origin in the complex plane
|z-w|

18. 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

19. 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.
Polar Coordinates - sin?
Complex numbers are points in the plane
natural
x-axis in the complex plane

20. Written as fractions - terminating + repeating decimals
Complex Addition
rational
How to multiply complex nubers(2+i)(2i-3)
Integers

21. (e^(iz) - e^(-iz)) / 2i
interchangeable
z1 ^ (z2)
Complex Numbers: Multiply
sin z

22. Real and imaginary numbers
Real Numbers
complex numbers
Subfield
How to multiply complex nubers(2+i)(2i-3)

23. The modulus of the complex number z= a + ib now can be interpreted as
Real and Imaginary Parts
Rational Number
the distance from z to the origin in the complex plane
Polar Coordinates - Multiplication by i

24. 1
conjugate pairs
Complex Numbers: Multiply
The Complex Numbers
i^4

25. (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)
Polar Coordinates - Multiplication by i
e^(ln z)
natural

26. Numbers on a numberline
Complex Numbers: Multiply
Imaginary Unit
Polar Coordinates - Multiplication
integers

27. A complex number and its conjugate
conjugate pairs
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
has a solution.
ln z

28. ½(e^(-y) +e^(y)) = cosh y
How to solve (2i+3)/(9-i)
cos iy
Euler Formula
i^2 = -1

29. For real a and b - a + bi =
Complex Number Formula
0 if and only if a = b = 0
Complex Exponentiation
standard form of complex numbers

30. z1z2* / |z2|²
imaginary
cosh²y - sinh²y
z1 / z2
Complex Exponentiation

31. A subset within a field.
Subfield
Integers
point of inflection
z + z*

32. When two complex numbers are multipiled together.
Complex Multiplication
can't get out of the complex numbers by adding (or subtracting) or multiplying two
standard form of complex numbers
irrational

33. The square root of -1.
Imaginary Unit
zz*
irrational
cos z

34. 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

35. ? = -tan?
Polar Coordinates - sin?
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Rational Number
Polar Coordinates - Arg(z*)

36. E ^ (z2 ln z1)
Affix
conjugate pairs
z1 ^ (z2)
Roots of Unity

37. Have radical
the distance from z to the origin in the complex plane
radicals
Euler's Formula
has a solution.

38. 3rd. Rule of Complex Arithmetic
Rules of Complex Arithmetic
point of inflection
Real and Imaginary Parts
For real a and b - a + bi = 0 if and only if a = b = 0

39. Equivalent to an Imaginary Unit.
Integers
z1 ^ (z2)
Imaginary number
imaginary

40. A+bi
Complex Number Formula
|z| = mod(z)
Any polynomial O(xn) - (n > 0)
cos iy

41. 1
z + z*
i²
Polar Coordinates - z
Complex Multiplication

42. 2a
v(-1)
multiplying complex numbers
z + z*
We say that c+di and c-di are complex conjugates.

43. The reals are just the
z1 ^ (z2)
Complex Subtraction
x-axis in the complex plane
Any polynomial O(xn) - (n > 0)

44. The complex number z representing a+bi.
Polar Coordinates - Division
standard form of complex numbers
Affix
cos z

45. 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

46. Divide moduli and subtract arguments
i^4
Polar Coordinates - Division
v(-1)
point of inflection

47. To simplify a complex fraction
0 if and only if a = b = 0
Complex Exponentiation
a real number: (a + bi)(a - bi) = a² + b²
multiply the numerator and the denominator by the complex conjugate of the denominator.

48. To simplify the square root of a negative number
Polar Coordinates - r
i^0
The Complex Numbers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

49. Imaginary number

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

50. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
conjugate
Imaginary number
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
cosh²y - sinh²y