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CLEP General Mathematics: Complex Numbers

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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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. In this amazing number field every algebraic equation in z with complex coefficients
Square Root
multiplying complex numbers
has a solution.
Polar Coordinates - z?¹

2. A subset within a field.
conjugate
Subfield
Polar Coordinates - Division
(cos? +isin?)n

3. 2a
x-axis in the complex plane
z + z*
Roots of Unity
Irrational Number

4. 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
multiply the numerator and the denominator by the complex conjugate of the denominator.
Imaginary number

5. Every complex number has the 'Standard Form':
i^3
Polar Coordinates - Multiplication by i
a + bi for some real a and b.
integers

6. 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
Imaginary Numbers
e^(ln z)
Complex Division

7. Like pi
transcendental
0 if and only if a = b = 0
sin iy
Euler's Formula

8. I^2 =
(cos? +isin?)n
-1
Square Root
How to add and subtract complex numbers (2-3i)-(4+6i)

9. Written as fractions - terminating + repeating decimals
rational
Roots of Unity
adding complex numbers
i^2 = -1

10. (a + bi) = (c + bi) =
(a + c) + ( b + d)i
Polar Coordinates - Division
radicals
Euler Formula

11. 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.
natural
How to find any Power
imaginary
How to multiply complex nubers(2+i)(2i-3)

12. R?¹(cos? - isin?)
transcendental
Polar Coordinates - Arg(z*)
i^1
Polar Coordinates - z?¹

13. The modulus of the complex number z= a + ib now can be interpreted as
x-axis in the complex plane
the distance from z to the origin in the complex plane
integers
Complex Addition

14. Numbers on a numberline
z - z*
multiplying complex numbers
adding complex numbers
integers

15. Imaginary number

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16. Root negative - has letter i
imaginary
rational
real
Imaginary number

17. 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
Polar Coordinates - Division
Imaginary Numbers
Field
subtracting complex numbers

18. Starts at 1 - does not include 0
complex numbers
natural
Complex Subtraction
z + z*

19. 1
x-axis in the complex plane
Polar Coordinates - Division
i^4
cos iy

20. The square root of -1.
Imaginary Unit
multiply the numerator and the denominator by the complex conjugate of the denominator.
conjugate pairs
(a + c) + ( b + d)i

21. The reals are just the
a real number: (a + bi)(a - bi) = a² + b²
x-axis in the complex plane
-1
sin iy

22. xpressions such as ``the complex number z'' - and ``the point z'' are now
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Absolute Value of a Complex Number
Roots of Unity
interchangeable

23. 1
Square Root
i^0
complex
Polar Coordinates - cos?

24. 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
conjugate pairs
Rules of Complex Arithmetic
De Moivre's Theorem
We say that c+di and c-di are complex conjugates.

25. E ^ (z2 ln z1)
z1 ^ (z2)
Square Root
irrational
Complex numbers are points in the plane

26. The complex number z representing a+bi.
Imaginary Unit
How to find any Power
Complex Number
Affix

27. A number that can be expressed as a fraction p/q where q is not equal to 0.
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
z1 ^ (z2)
How to add and subtract complex numbers (2-3i)-(4+6i)
Rational Number

28. 4th. Rule of Complex Arithmetic
How to find any Power
x-axis in the complex plane
(a + bi) = (c + bi) = (a + c) + ( b + d)i
point of inflection

29. (a + bi)(c + bi) =
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
(a + c) + ( b + d)i
Polar Coordinates - r
conjugate

30. 1
radicals
ln z
Imaginary Numbers
i^2

31. 2nd. Rule of Complex Arithmetic

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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
Complex Numbers: Add & subtract
can't get out of the complex numbers by adding (or subtracting) or multiplying two
four different numbers: i - -i - 1 - and -1.
Complex Addition

33. Cos n? + i sin n? (for all n integers)
(cos? +isin?)n
i^2
Polar Coordinates - cos?
Complex Multiplication

34. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
e^(ln z)
How to add and subtract complex numbers (2-3i)-(4+6i)
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
the distance from z to the origin in the complex plane

35. When two complex numbers are multipiled together.
conjugate pairs
Complex Multiplication
Polar Coordinates - z
The Complex Numbers

36. ½(e^(iz) + e^(-iz))
Rules of Complex Arithmetic
complex numbers
cos z
Field

37. Real and imaginary numbers
Polar Coordinates - Arg(z*)
complex numbers
ln z
zz*

38. z1z2* / |z2|²
a real number: (a + bi)(a - bi) = a² + b²
real
sin iy
z1 / z2

39. Rotates anticlockwise by p/2
i²
the distance from z to the origin in the complex plane
Polar Coordinates - Multiplication by i
cos z

40. (e^(-y) - e^(y)) / 2i = i sinh y
sin iy
Complex Conjugate
point of inflection
De Moivre's Theorem

41. Where the curvature of the graph changes
z1 / z2
point of inflection
i^3
cosh²y - sinh²y

42. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
i^0
Field
Polar Coordinates - Multiplication
conjugate

43. Have radical
real
radicals
How to add and subtract complex numbers (2-3i)-(4+6i)
Complex Numbers: Multiply

44. All numbers
complex
Every complex number has the 'Standard Form': a + bi for some real a and b.
Complex Conjugate
interchangeable

45. We see in this way that the distance between two points z and w in the complex plane is
Irrational Number
e^(ln z)
Polar Coordinates - Division
|z-w|

46. When two complex numbers are added together.
Complex numbers are points in the plane
Complex Addition
i²
Integers

47. A number that cannot be expressed as a fraction for any integer.
How to multiply complex nubers(2+i)(2i-3)
z + z*
i^2 = -1
Irrational Number

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

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49. No i
real
point of inflection
Complex numbers are points in the plane
rational

50. To simplify the square root of a negative number
Polar Coordinates - Division
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Complex Division