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. All the powers of i can be written as
has a solution.
De Moivre's Theorem
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
four different numbers: i - -i - 1 - and -1.

2. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

3. When two complex numbers are multipiled together.
conjugate pairs
cosh²y - sinh²y
Complex Multiplication
cos iy

4. 2a
Square Root
i^0
natural
z + z*

5. 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.
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
multiplying complex numbers
Complex Numbers: Multiply

6. We see in this way that the distance between two points z and w in the complex plane is
|z-w|
For real a and b - a + bi = 0 if and only if a = b = 0
the complex numbers
four different numbers: i - -i - 1 - and -1.

7. (a + bi)(c + bi) =
real
Rules of Complex Arithmetic
Euler Formula
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

8. Written as fractions - terminating + repeating decimals
rational
Rules of Complex Arithmetic
i^2 = -1
Liouville's Theorem -

9. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
Rules of Complex Arithmetic
standard form of complex numbers
ln z
Complex Multiplication

10. 2ib
complex
z - z*
standard form of complex numbers
Complex Exponentiation

11. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
v(-1)
Roots of Unity
i^1
Complex Numbers: Multiply

12. In this amazing number field every algebraic equation in z with complex coefficients
Polar Coordinates - sin?
has a solution.
Euler's Formula
Complex Addition

13. Real and imaginary numbers
complex numbers
cosh²y - sinh²y
|z-w|
radicals

14. Derives z = a+bi
rational
z + z*
Euler Formula
zz*

15. No i
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Polar Coordinates - cos?
'i'
real

16. The product of an imaginary number and its conjugate is
a real number: (a + bi)(a - bi) = a² + b²
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
conjugate
Imaginary Numbers

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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

18. I^2 =
(cos? +isin?)n
The Complex Numbers
-1
Imaginary Numbers

19. R^2 = x
i^3
interchangeable
Square Root
transcendental

20. 1
i^0
Complex numbers are points in the plane
Complex Number Formula
a + bi for some real a and b.

21. 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
Irrational Number
four different numbers: i - -i - 1 - and -1.
Complex numbers are points in the plane

22. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
How to add and subtract complex numbers (2-3i)-(4+6i)
Real Numbers
Complex Multiplication
transcendental

23. z1z2* / |z2|²
z1 / z2
imaginary
|z-w|
z + z*

24. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
natural
Imaginary number
rational
conjugate

25. The modulus of the complex number z= a + ib now can be interpreted as
|z-w|
complex numbers
the distance from z to the origin in the complex plane
How to add and subtract complex numbers (2-3i)-(4+6i)

26. 3rd. Rule of Complex Arithmetic
|z| = mod(z)
For real a and b - a + bi = 0 if and only if a = b = 0
i^2
Polar Coordinates - Division

27. A² + b² - real and non negative
i^0
cos z
Complex Numbers: Multiply
zz*

28. To simplify a complex fraction
Any polynomial O(xn) - (n > 0)
Complex Division
Absolute Value of a Complex Number
multiply the numerator and the denominator by the complex conjugate of the denominator.

29. The reals are just the
x-axis in the complex plane
(a + c) + ( b + d)i
radicals
Complex Exponentiation

30. Cos n? + i sin n? (for all n integers)
standard form of complex numbers
ln z
(cos? +isin?)n
point of inflection

31. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
z1 / z2
Field
subtracting complex numbers
Complex Numbers: Multiply

32. When two complex numbers are added together.
transcendental
Complex Addition
a + bi for some real a and b.
Complex Subtraction

33. 1
Complex Conjugate
complex
i^4
rational

34. 5th. Rule of Complex Arithmetic
How to solve (2i+3)/(9-i)
How to find any Power
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Any polynomial O(xn) - (n > 0)

35. For real a and b - a + bi =
sin z
0 if and only if a = b = 0
four different numbers: i - -i - 1 - and -1.
For real a and b - a + bi = 0 if and only if a = b = 0

36. 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
cos z
Polar Coordinates - r
has a solution.

37. All numbers
How to multiply complex nubers(2+i)(2i-3)
Polar Coordinates - r
complex
Complex Number Formula

38. We can also think of the point z= a+ ib as
the complex numbers
Imaginary Numbers
z + z*
the vector (a -b)

39. V(zz*) = v(a² + b²)
z + z*
z1 / z2
|z| = mod(z)
conjugate

40. A + bi
v(-1)
standard form of complex numbers
the distance from z to the origin in the complex plane
i^3

41. 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
Euler Formula
ln z
Rules of Complex Arithmetic
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

42. Starts at 1 - does not include 0
a real number: (a + bi)(a - bi) = a² + b²
Rules of Complex Arithmetic
'i'
natural

43. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
Complex Number Formula
Integers
v(-1)
Polar Coordinates - z?¹

44. A subset within a field.
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Conjugate
Subfield
Roots of Unity

45. When two complex numbers are subtracted from one another.
Complex Subtraction
sin z
a + bi for some real a and b.
Polar Coordinates - Division

46. (a + bi) = (c + bi) =
(a + c) + ( b + d)i
z + z*
Polar Coordinates - Arg(z*)
Absolute Value of a Complex Number

47. The field of all rational and irrational numbers.
Euler Formula
has a solution.
Real Numbers
z - z*

48. Have radical
radicals
Complex Subtraction
Complex Exponentiation
Any polynomial O(xn) - (n > 0)

49. (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
How to add and subtract complex numbers (2-3i)-(4+6i)
|z| = mod(z)
How to solve (2i+3)/(9-i)
a + bi for some real a and b.

50. xpressions such as ``the complex number z'' - and ``the point z'' are now
interchangeable
Roots of Unity
multiplying complex numbers
integers