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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. R^2 = x
How to multiply complex nubers(2+i)(2i-3)
transcendental
Square Root
Affix

2. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Every complex number has the 'Standard Form': a + bi for some real a and b.
Absolute Value of a Complex Number
natural
Complex Number

3. Imaginary number

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4. The square root of -1.
imaginary
Imaginary Unit
Complex Multiplication
has a solution.

5. ? = -tan?
z1 / z2
Any polynomial O(xn) - (n > 0)
Polar Coordinates - Arg(z*)
zz*

6. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
the distance from z to the origin in the complex plane
Polar Coordinates - sin?
cos z
Integers

7. V(zz*) = v(a² + b²)
Polar Coordinates - z
|z| = mod(z)
Polar Coordinates - Multiplication by i
multiplying complex numbers

8. The product of an imaginary number and its conjugate is
a real number: (a + bi)(a - bi) = a² + b²
has a solution.
can't get out of the complex numbers by adding (or subtracting) or multiplying two
point of inflection

9. The reals are just the
e^(ln z)
Complex Multiplication
adding complex numbers
x-axis in the complex plane

10. Any number not rational
z - z*
(cos? +isin?)n
complex numbers
irrational

11. 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.
cos z
Complex Numbers: Multiply
radicals
the complex numbers

12. When two complex numbers are added together.
Complex Addition
non-integers
Irrational Number
We say that c+di and c-di are complex conjugates.

13. 1st. Rule of Complex Arithmetic
complex numbers
Rational Number
'i'
i^2 = -1

14. 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
multiply the numerator and the denominator by the complex conjugate of the denominator.
i^0

15. (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
z1 ^ (z2)
(a + bi) = (c + bi) = (a + c) + ( b + d)i
irrational
How to multiply complex nubers(2+i)(2i-3)

16. A subset within a field.
Real Numbers
Irrational Number
a real number: (a + bi)(a - bi) = a² + b²
Subfield

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
Imaginary number
|z| = mod(z)
We say that c+di and c-di are complex conjugates.
four different numbers: i - -i - 1 - and -1.

18. (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
standard form of complex numbers
Irrational Number
How to solve (2i+3)/(9-i)
i^2 = -1

19. Have radical
radicals
the vector (a -b)
conjugate
subtracting complex numbers

20. I^2 =
Field
Complex Number
conjugate
-1

21. (a + bi) = (c + bi) =
conjugate
(a + c) + ( b + d)i
a + bi for some real a and b.
|z| = mod(z)

22. For real a and b - a + bi =
z1 / z2
|z-w|
0 if and only if a = b = 0
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

23. Not on the numberline
transcendental
real
non-integers
How to solve (2i+3)/(9-i)

24. Real and imaginary numbers
complex numbers
(a + bi) = (c + bi) = (a + c) + ( b + d)i
a + bi for some real a and b.
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

25. x / r
rational
Polar Coordinates - cos?
How to add and subtract complex numbers (2-3i)-(4+6i)
standard form of complex numbers

26. Equivalent to an Imaginary Unit.
Imaginary number
i^4
De Moivre's Theorem
Square Root

27. ½(e^(-y) +e^(y)) = cosh y
i^3
radicals
cos iy
has a solution.

28. Like pi
i²
Complex Conjugate
transcendental
imaginary

29. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
Square Root
How to add and subtract complex numbers (2-3i)-(4+6i)
(cos? +isin?)n
Complex Number

30. All the powers of i can be written as
The Complex Numbers
Complex Conjugate
four different numbers: i - -i - 1 - and -1.
radicals

31. y / r
cosh²y - sinh²y
i^2
Polar Coordinates - sin?
Irrational Number

32. 1
sin z
irrational
i^2 = -1
cosh²y - sinh²y

33. 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.'
irrational
Complex Number
subtracting complex numbers
Roots of Unity

34. (a + bi)(c + bi) =
i²
Irrational Number
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Liouville's Theorem -

35. When two complex numbers are divided.
z1 ^ (z2)
Complex Division
Complex Addition
conjugate

36. 1
i^0
subtracting complex numbers
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Complex Addition

37. Numbers on a numberline
e^(ln z)
i^1
non-integers
integers

38. 5th. Rule of Complex Arithmetic
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Square Root
sin iy
i^4

39. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Field
i^2
a + bi for some real a and b.
Roots of Unity

40. 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
multiply the numerator and the denominator by the complex conjugate of the denominator.
z - z*
Argand diagram
the complex numbers

41. A complex number and its conjugate
radicals
Complex Exponentiation
conjugate pairs
point of inflection

42. A + bi
complex numbers
How to find any Power
multiply the numerator and the denominator by the complex conjugate of the denominator.
standard form of complex numbers

43. When two complex numbers are subtracted from one another.
Complex Subtraction
radicals
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
|z| = mod(z)

44. The modulus of the complex number z= a + ib now can be interpreted as
sin iy
Liouville's Theorem -
the distance from z to the origin in the complex plane
z1 ^ (z2)

45. A number that cannot be expressed as a fraction for any integer.
complex
Irrational Number
integers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

46. I = imaginary unit - i² = -1 or i = v-1
multiply the numerator and the denominator by the complex conjugate of the denominator.
Complex Subtraction
x-axis in the complex plane
Imaginary Numbers

47. 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
Complex Addition
Real and Imaginary Parts
cosh²y - sinh²y
x-axis in the complex plane

48. Given (4-2i) the complex conjugate would be (4+2i)
Complex Conjugate
complex numbers
point of inflection
Complex Number Formula

49. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
multiplying complex numbers
Polar Coordinates - Multiplication
irrational
Euler's Formula

50. 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
Any polynomial O(xn) - (n > 0)
i²
z + z*
Complex Numbers: Add & subtract