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CLEP General Mathematics: Complex Numbers

Subjects : clep, math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Divide moduli and subtract arguments
Polar Coordinates - Division
Complex Conjugate
How to find any Power
For real a and b - a + bi = 0 if and only if a = b = 0

2. When two complex numbers are added together.
Roots of Unity
Affix
Polar Coordinates - Multiplication by i
Complex Addition

3. A+bi
Euler's Formula
'i'
Subfield
Complex Number Formula

4. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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5. All the powers of i can be written as
Polar Coordinates - z
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Polar Coordinates - Arg(z*)
four different numbers: i - -i - 1 - and -1.

6. 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
Complex Numbers: Add & subtract
Complex Subtraction
i^4
i^3

7. 3
Complex Number
i^3
interchangeable
multiplying complex numbers

8. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
imaginary
i^0
How to add and subtract complex numbers (2-3i)-(4+6i)
z - z*

9. I
v(-1)
four different numbers: i - -i - 1 - and -1.
0 if and only if a = b = 0
transcendental

10. Imaginary number

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11. A number that can be expressed as a fraction p/q where q is not equal to 0.
i^0
Square Root
Complex Number
Rational Number

12. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
ln z
sin iy
zz*
multiplying complex numbers

13. 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.
Complex numbers are points in the plane
v(-1)
Every complex number has the 'Standard Form': a + bi for some real a and b.
i^0

14. When two complex numbers are divided.
Complex Division
non-integers
zz*
Real Numbers

15. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
Integers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
subtracting complex numbers
Roots of Unity

16. E ^ (z2 ln z1)
The Complex Numbers
sin iy
the complex numbers
z1 ^ (z2)

17. 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 Number Formula
We say that c+di and c-di are complex conjugates.
irrational
z1 ^ (z2)

18. Like pi
ln z
transcendental
integers
i^4

19. 1
cosh²y - sinh²y
cos z
Euler's Formula
Polar Coordinates - z

20. Not on the numberline
Field
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Imaginary number
non-integers

21. 3rd. Rule of Complex Arithmetic
Square Root
subtracting complex numbers
For real a and b - a + bi = 0 if and only if a = b = 0
Polar Coordinates - Division

22. 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.
standard form of complex numbers
z - z*
How to find any Power
(a + bi) = (c + bi) = (a + c) + ( b + d)i

23. 1
i^0
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Absolute Value of a Complex Number
multiplying complex numbers

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

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25. (a + bi) = (c + bi) =
real
Complex Numbers: Add & subtract
the complex numbers
(a + c) + ( b + d)i

26. When two complex numbers are multipiled together.
Complex Multiplication
Polar Coordinates - Division
Subfield
four different numbers: i - -i - 1 - and -1.

27. (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
Real and Imaginary Parts
cosh²y - sinh²y
How to solve (2i+3)/(9-i)
complex

28. z1z2* / |z2|²
sin iy
i^4
Absolute Value of a Complex Number
z1 / z2

29. 1
Complex Subtraction
i²
point of inflection
imaginary

30. Written as fractions - terminating + repeating decimals
Every complex number has the 'Standard Form': a + bi for some real a and b.
conjugate
a real number: (a + bi)(a - bi) = a² + b²
rational

31. A plot of complex numbers as points.
Square Root
De Moivre's Theorem
Argand diagram
Rules of Complex Arithmetic

32. Numbers on a numberline
complex
the vector (a -b)
integers
Complex Multiplication

33. (a + bi)(c + bi) =
The Complex Numbers
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Subtraction

34. In this amazing number field every algebraic equation in z with complex coefficients
Euler's Formula
cos iy
Any polynomial O(xn) - (n > 0)
has a solution.

35. Root negative - has letter i
z - z*
imaginary
For real a and b - a + bi = 0 if and only if a = b = 0
Real Numbers

36. The modulus of the complex number z= a + ib now can be interpreted as
How to solve (2i+3)/(9-i)
'i'
How to multiply complex nubers(2+i)(2i-3)
the distance from z to the origin in the complex plane

37. 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
Complex Numbers: Multiply
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Imaginary Numbers

38. Equivalent to an Imaginary Unit.
Imaginary number
Polar Coordinates - Division
Every complex number has the 'Standard Form': a + bi for some real a and b.
Polar Coordinates - z

39. I = imaginary unit - i² = -1 or i = v-1
Imaginary Numbers
z + z*
How to add and subtract complex numbers (2-3i)-(4+6i)
standard form of complex numbers

40. Multiply moduli and add arguments
Polar Coordinates - Multiplication
multiplying complex numbers
four different numbers: i - -i - 1 - and -1.
z + z*

41. 5th. Rule of Complex Arithmetic
conjugate
i^3
For real a and b - a + bi = 0 if and only if a = b = 0
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

42. 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.'
v(-1)
|z| = mod(z)
Complex Number
conjugate pairs

43. 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.
Field
De Moivre's Theorem
z + z*
Complex Numbers: Multiply

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
adding complex numbers
subtracting complex numbers
Subfield
ln z

45. A subset within a field.
Irrational Number
Subfield
Rules of Complex Arithmetic
Complex Numbers: Add & subtract

46. A + bi
standard form of complex numbers
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Polar Coordinates - r
Euler's Formula

47. A² + b² - real and non negative
x-axis in the complex plane
sin z
i^2 = -1
zz*

48. Derives z = a+bi
Euler's Formula
Euler Formula
irrational
Polar Coordinates - Arg(z*)

49. Any number not rational
Any polynomial O(xn) - (n > 0)
radicals
irrational
i^2

50. (e^(-y) - e^(y)) / 2i = i sinh y
Imaginary number
sin iy
Complex Number Formula
Polar Coordinates - Multiplication by i

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CLEP General Mathematics: Complex Numbers

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