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. Not on the numberline
complex
cosh²y - sinh²y
ln z
non-integers

2. R?¹(cos? - isin?)
i^2 = -1
The Complex Numbers
complex
Polar Coordinates - z?¹

3. 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

4. In this amazing number field every algebraic equation in z with complex coefficients
multiplying complex numbers
can't get out of the complex numbers by adding (or subtracting) or multiplying two
has a solution.
subtracting complex numbers

5. A+bi
Complex Number Formula
Liouville's Theorem -
Polar Coordinates - Arg(z*)
subtracting complex numbers

6. We can also think of the point z= a+ ib as
cos z
complex
Affix
the vector (a -b)

7. I^2 =
Affix
-1
a + bi for some real a and b.
Argand diagram

8. 1
Complex Number Formula
point of inflection
i²
Polar Coordinates - Division

9. A number that cannot be expressed as a fraction for any integer.
adding complex numbers
Irrational Number
Polar Coordinates - Multiplication by i
Imaginary Unit

10. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
cos iy
Irrational Number
Real and Imaginary Parts
How to add and subtract complex numbers (2-3i)-(4+6i)

11. A complex number may be taken to the power of another complex number.
Complex Exponentiation
|z-w|
-1
natural

12. Cos n? + i sin n? (for all n integers)
Rational Number
Field
Argand diagram
(cos? +isin?)n

13. All numbers
i^4
imaginary
e^(ln z)
complex

14. Divide moduli and subtract arguments
i²
Polar Coordinates - Division
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Polar Coordinates - r

15. The square root of -1.
Imaginary Unit
Polar Coordinates - Multiplication by i
Rules of Complex Arithmetic
How to multiply complex nubers(2+i)(2i-3)

16. 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
integers
Rules of Complex Arithmetic
v(-1)
Real Numbers

17. x + iy = r(cos? + isin?) = re^(i?)
non-integers
Polar Coordinates - z
Polar Coordinates - Multiplication by i
Complex Subtraction

18. 1
Complex numbers are points in the plane
-1
cosh²y - sinh²y
Polar Coordinates - cos?

19. E ^ (z2 ln z1)
i²
Rational Number
cos iy
z1 ^ (z2)

20. y / r
Polar Coordinates - sin?
We say that c+di and c-di are complex conjugates.
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
multiply the numerator and the denominator by the complex conjugate of the denominator.

21. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
Polar Coordinates - z?¹
conjugate
imaginary
i^1

22. Numbers on a numberline
the complex numbers
z + z*
sin iy
integers

23. To simplify a complex fraction
multiply the numerator and the denominator by the complex conjugate of the denominator.
the distance from z to the origin in the complex plane
(a + bi) = (c + bi) = (a + c) + ( b + d)i
multiplying complex numbers

24. Multiply moduli and add arguments
a + bi for some real a and b.
We say that c+di and c-di are complex conjugates.
Euler's Formula
Polar Coordinates - Multiplication

25. ½(e^(-y) +e^(y)) = cosh y
Complex Exponentiation
cos iy
i²
Imaginary Unit

26. 1
Polar Coordinates - Arg(z*)
multiply the numerator and the denominator by the complex conjugate of the denominator.
i^2
Complex Number Formula

27. 1
i^0
complex numbers
point of inflection
Complex Number Formula

28. For real a and b - a + bi =
0 if and only if a = b = 0
Complex Subtraction
Polar Coordinates - z
cosh²y - sinh²y

29. The complex number z representing a+bi.
Affix
multiply the numerator and the denominator by the complex conjugate of the denominator.
the distance from z to the origin in the complex plane
complex numbers

30. 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
Affix
Real and Imaginary Parts
adding complex numbers
Any polynomial O(xn) - (n > 0)

31. No i
Argand diagram
real
i^1
conjugate

32. The product of an imaginary number and its conjugate is
|z| = mod(z)
Polar Coordinates - Multiplication by i
i^2 = -1
a real number: (a + bi)(a - bi) = a² + b²

33. Any number not rational
Complex Number
Imaginary number
irrational
Complex Multiplication

34. ? = -tan?
-1
Polar Coordinates - Arg(z*)
conjugate pairs
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

35. I
-1
zz*
v(-1)
How to multiply complex nubers(2+i)(2i-3)

36. Imaginary number

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

37. Every complex number has the 'Standard Form':
multiply the numerator and the denominator by the complex conjugate of the denominator.
(a + c) + ( b + d)i
a + bi for some real a and b.
Complex Number

38. Given (4-2i) the complex conjugate would be (4+2i)
Complex Conjugate
non-integers
Every complex number has the 'Standard Form': a + bi for some real a and b.
How to add and subtract complex numbers (2-3i)-(4+6i)

39. Equivalent to an Imaginary Unit.
How to find any Power
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Imaginary number
multiply the numerator and the denominator by the complex conjugate of the denominator.

40. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
ln z
Complex Numbers: Multiply
For real a and b - a + bi = 0 if and only if a = b = 0
Complex numbers are points in the plane

41. (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
a + bi for some real a and b.
How to multiply complex nubers(2+i)(2i-3)
imaginary
the vector (a -b)

42. When two complex numbers are multipiled together.
Complex Multiplication
the vector (a -b)
Rules of Complex Arithmetic
z1 / z2

43. Root negative - has letter i
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
can't get out of the complex numbers by adding (or subtracting) or multiplying two
cos iy
imaginary

44. 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
conjugate
four different numbers: i - -i - 1 - and -1.
adding complex numbers
zz*

45. R^2 = x
Complex numbers are points in the plane
Real Numbers
i^2 = -1
Square Root

46. ½(e^(iz) + e^(-iz))
a + bi for some real a and b.
cos z
rational
|z-w|

47. 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
e^(ln z)
integers
Imaginary number

48. When two complex numbers are subtracted from one another.
Square Root
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Complex Subtraction
conjugate pairs

49. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
Integers
cos iy
The Complex Numbers
Complex Division

50. 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
Complex Subtraction
subtracting complex numbers
sin z
How to solve (2i+3)/(9-i)