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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. Numbers on a numberline
z1 ^ (z2)
integers
the vector (a -b)
Complex Multiplication

2. All numbers
complex
cos iy
Subfield
rational

3. Derives z = a+bi
Polar Coordinates - Division
multiplying complex numbers
Euler Formula
(a + c) + ( b + d)i

4. Written as fractions - terminating + repeating decimals
sin z
-1
the complex numbers
rational

5. 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
Polar Coordinates - Arg(z*)
adding complex numbers
subtracting complex numbers
|z| = mod(z)

6. The complex number z representing a+bi.
Affix
How to multiply complex nubers(2+i)(2i-3)
Complex Number Formula
0 if and only if a = b = 0

7. A complex number and its conjugate
conjugate pairs
sin z
Euler Formula
Square Root

8. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
the vector (a -b)
multiply the numerator and the denominator by the complex conjugate of the denominator.
How to add and subtract complex numbers (2-3i)-(4+6i)
|z| = mod(z)

9. 1
z1 / z2
i²
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
How to multiply complex nubers(2+i)(2i-3)

10. I = imaginary unit - i² = -1 or i = v-1
complex numbers
Imaginary Numbers
i^2
Euler Formula

11. 1
subtracting complex numbers
cosh²y - sinh²y
cos iy
For real a and b - a + bi = 0 if and only if a = b = 0

12. Like pi
transcendental
the vector (a -b)
How to add and subtract complex numbers (2-3i)-(4+6i)
non-integers

13. 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.
|z| = mod(z)
How to solve (2i+3)/(9-i)
a real number: (a + bi)(a - bi) = a² + b²
How to find any Power

14. Multiply moduli and add arguments
i^2 = -1
Polar Coordinates - Multiplication
For real a and b - a + bi = 0 if and only if a = b = 0
i²

15. Divide moduli and subtract arguments
Polar Coordinates - Division
adding complex numbers
Affix
Complex Exponentiation

16. Imaginary number

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17. For real a and b - a + bi =
z1 / z2
ln z
0 if and only if a = b = 0
can't get out of the complex numbers by adding (or subtracting) or multiplying two

18. A plot of complex numbers as points.
conjugate
cosh²y - sinh²y
Argand diagram
Polar Coordinates - z

19. x / r
ln z
the distance from z to the origin in the complex plane
conjugate
Polar Coordinates - cos?

20. 2ib
z - z*
Irrational Number
Complex Subtraction
Complex Multiplication

21. A subset within a field.
rational
interchangeable
Rules of Complex Arithmetic
Subfield

22. 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
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Complex numbers are points in the plane
i^2 = -1

23. 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.'
We say that c+di and c-di are complex conjugates.
Complex Number
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Polar Coordinates - Multiplication

24. I^2 =
Polar Coordinates - sin?
-1
a real number: (a + bi)(a - bi) = a² + b²
De Moivre's Theorem

25. 3rd. Rule of Complex Arithmetic
For real a and b - a + bi = 0 if and only if a = b = 0
Polar Coordinates - Division
can't get out of the complex numbers by adding (or subtracting) or multiplying two
cos iy

26. 2nd. Rule of Complex Arithmetic

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27. xpressions such as ``the complex number z'' - and ``the point z'' are now
interchangeable
Argand diagram
z1 ^ (z2)
Complex numbers are points in the plane

28. A+bi
interchangeable
Complex Number Formula
conjugate
Complex Exponentiation

29. (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 solve (2i+3)/(9-i)
cos z
complex
How to multiply complex nubers(2+i)(2i-3)

30. 1
z + z*
natural
i²
i^0

31. V(x² + y²) = |z|
Polar Coordinates - r
De Moivre's Theorem
i^2
Complex Multiplication

32. A number that can be expressed as a fraction p/q where q is not equal to 0.
'i'
the vector (a -b)
integers
Rational Number

33. When two complex numbers are added together.
multiplying complex numbers
Complex Number Formula
Complex Addition
Complex numbers are points in the plane

34. (a + bi)(c + bi) =
The Complex Numbers
Polar Coordinates - Multiplication by i
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Rational Number

35. The reals are just the
i^0
x-axis in the complex plane
z1 ^ (z2)
cos z

36. A complex number may be taken to the power of another complex number.
point of inflection
Complex Exponentiation
multiply the numerator and the denominator by the complex conjugate of the denominator.
Polar Coordinates - r

37. To prove that number field every algebraic equation in z with complex coefficients has a solution we need

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38. The modulus of the complex number z= a + ib now can be interpreted as
i²
the distance from z to the origin in the complex plane
Real Numbers
Complex Addition

39. A number that cannot be expressed as a fraction for any integer.
natural
Argand diagram
Irrational Number
transcendental

40. The square root of -1.
subtracting complex numbers
Imaginary Unit
Complex Division
zz*

41. 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
Square Root
complex
sin z
the complex numbers

42. The field of all rational and irrational numbers.
z + z*
zz*
Polar Coordinates - cos?
Real Numbers

43. No i
We say that c+di and c-di are complex conjugates.
Complex Number Formula
real
The Complex Numbers

44. The product of an imaginary number and its conjugate is
Polar Coordinates - Multiplication by i
a real number: (a + bi)(a - bi) = a² + b²
(a + c) + ( b + d)i
Argand diagram

45. When two complex numbers are multipiled together.
Complex Multiplication
cos z
irrational
Subfield

46. 4th. Rule of Complex Arithmetic
i^2 = -1
zz*
Complex Numbers: Multiply
(a + bi) = (c + bi) = (a + c) + ( b + d)i

47. Cos n? + i sin n? (for all n integers)
Euler's Formula
'i'
(cos? +isin?)n
Square Root

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

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49. V(zz*) = v(a² + b²)
|z| = mod(z)
Real Numbers
i^3
Polar Coordinates - Multiplication by i

50. To simplify the square root of a negative number
rational
Liouville's Theorem -
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
De Moivre's Theorem