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. When two complex numbers are subtracted from one another.
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Euler Formula
Complex Subtraction
Complex Division

2. All numbers
Polar Coordinates - sin?
Polar Coordinates - Arg(z*)
z + z*
complex

3. 3
|z-w|
multiplying complex numbers
i^2 = -1
i^3

4. (a + bi) = (c + bi) =
Polar Coordinates - z
Polar Coordinates - Multiplication by i
(a + c) + ( b + d)i
a real number: (a + bi)(a - bi) = a² + b²

5. The complex number z representing a+bi.
Affix
Imaginary number
Roots of Unity
sin iy

6. R?¹(cos? - isin?)
the complex numbers
Polar Coordinates - z?¹
(cos? +isin?)n
Integers

7. 1st. Rule of Complex Arithmetic
z - z*
v(-1)
non-integers
i^2 = -1

8. The reals are just the
z1 ^ (z2)
conjugate pairs
x-axis in the complex plane
How to find any Power

9. Not on the numberline
ln z
non-integers
Complex Number
complex numbers

10. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Absolute Value of a Complex Number
Roots of Unity
Complex Number
imaginary

11. 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.'
Complex Number
a real number: (a + bi)(a - bi) = a² + b²
How to solve (2i+3)/(9-i)
Rational Number

12. To simplify a complex fraction
the complex numbers
Polar Coordinates - z
multiply the numerator and the denominator by the complex conjugate of the denominator.
imaginary

13. A number that can be expressed as a fraction p/q where q is not equal to 0.
e^(ln z)
zz*
sin iy
Rational Number

14. 3rd. Rule of Complex Arithmetic
-1
For real a and b - a + bi = 0 if and only if a = b = 0
0 if and only if a = b = 0
Complex Number

15. Given (4-2i) the complex conjugate would be (4+2i)
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Imaginary Unit
Complex Conjugate
z1 ^ (z2)

16. A subset within a field.
has a solution.
Irrational Number
Subfield
e^(ln z)

17. Where the curvature of the graph changes
zz*
point of inflection
Euler's Formula
conjugate

18. Have radical
has a solution.
Roots of Unity
radicals
Polar Coordinates - cos?

19. When two complex numbers are multipiled together.
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Subfield
Imaginary Unit
Complex Multiplication

20. 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 - sin?
adding complex numbers
i^2
complex

21. A complex number and its conjugate
Polar Coordinates - z
Complex Conjugate
conjugate pairs
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

22. A complex number may be taken to the power of another complex number.
Polar Coordinates - Division
Complex Exponentiation
Polar Coordinates - Arg(z*)
rational

23. All the powers of i can be written as
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
z - z*
v(-1)
four different numbers: i - -i - 1 - and -1.

24. We can also think of the point z= a+ ib as
the vector (a -b)
Polar Coordinates - Division
(a + c) + ( b + d)i
Imaginary Numbers

25. Derives z = a+bi
Euler Formula
Polar Coordinates - Multiplication by i
Euler's Formula
integers

26. When two complex numbers are added together.
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Addition
How to find any Power

27. Starts at 1 - does not include 0
adding complex numbers
x-axis in the complex plane
natural
i^1

28. I = imaginary unit - i² = -1 or i = v-1
complex numbers
Imaginary Numbers
four different numbers: i - -i - 1 - and -1.
has a solution.

29. Any number not rational
standard form of complex numbers
radicals
natural
irrational

30. E ^ (z2 ln z1)
z1 ^ (z2)
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Polar Coordinates - z?¹
irrational

31. The square root of -1.
Complex Number Formula
Imaginary Numbers
Roots of Unity
Imaginary Unit

32. Has exactly n roots by the fundamental theorem of algebra
cos iy
-1
Any polynomial O(xn) - (n > 0)
four different numbers: i - -i - 1 - and -1.

33. (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
v(-1)
a + bi for some real a and b.
How to solve (2i+3)/(9-i)
subtracting complex numbers

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

35. Multiply moduli and add arguments
Polar Coordinates - Multiplication
Euler Formula
Complex numbers are points in the plane
Euler's Formula

36. ½(e^(-y) +e^(y)) = cosh y
multiply the numerator and the denominator by the complex conjugate of the denominator.
rational
cos iy
ln z

37. A number that cannot be expressed as a fraction for any integer.
Irrational Number
zz*
z1 / z2
sin z

38. Written as fractions - terminating + repeating decimals
Complex Conjugate
complex
rational
conjugate

39. (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
sin iy
complex
How to multiply complex nubers(2+i)(2i-3)
z1 ^ (z2)

40. The field of all rational and irrational numbers.
Rules of Complex Arithmetic
Real Numbers
Polar Coordinates - sin?
Roots of Unity

41. Numbers on a numberline
i^1
integers
|z| = mod(z)
conjugate

42. R^2 = x
Square Root
For real a and b - a + bi = 0 if and only if a = b = 0
v(-1)
rational

43. 1
integers
Complex Number Formula
Imaginary Numbers
cosh²y - sinh²y

44. V(zz*) = v(a² + b²)
Polar Coordinates - cos?
natural
Any polynomial O(xn) - (n > 0)
|z| = mod(z)

45. Real and imaginary numbers
Polar Coordinates - z?¹
complex numbers
the complex numbers
Square Root

46. Cos n? + i sin n? (for all n integers)
cos z
Square Root
z - z*
(cos? +isin?)n

47. E^(ln r) e^(i?) e^(2pin)
ln z
Complex Numbers: Multiply
e^(ln z)
How to find any Power

48. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
four different numbers: i - -i - 1 - and -1.
Integers
(cos? +isin?)n
z1 ^ (z2)

49. I
sin z
0 if and only if a = b = 0
Complex Conjugate
i^1

50. I
Polar Coordinates - Arg(z*)
transcendental
v(-1)
interchangeable