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. Multiply moduli and add arguments
(a + bi) = (c + bi) = (a + c) + ( b + d)i
sin iy
Polar Coordinates - Multiplication
Complex numbers are points in the plane

2. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
Polar Coordinates - Multiplication by i
Real and Imaginary Parts
ln z
radicals

3. 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
irrational
adding complex numbers
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

4. 1
The Complex Numbers
Complex Subtraction
Field
i^4

5. 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

6. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
Complex Numbers: Multiply
interchangeable
Field
ln z

7. The square root of -1.
Real Numbers
Polar Coordinates - cos?
zz*
Imaginary Unit

8. A complex number and its conjugate
conjugate pairs
(cos? +isin?)n
the complex numbers
zz*

9. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
natural
the distance from z to the origin in the complex plane
Integers
i^0

10. 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
adding complex numbers
the complex numbers
i^2
has a solution.

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

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

12. Derives z = a+bi
Euler Formula
cosh²y - sinh²y
z1 ^ (z2)
Polar Coordinates - Arg(z*)

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.
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Complex Number
How to find any Power
zz*

14. y / r
cosh²y - sinh²y
Complex Numbers: Multiply
point of inflection
Polar Coordinates - sin?

15. 1
i²
conjugate pairs
|z| = mod(z)
Complex Multiplication

16. 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.
Irrational Number
Complex Number
Complex Numbers: Multiply
subtracting complex numbers

17. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
i²
i^3
How to add and subtract complex numbers (2-3i)-(4+6i)
(a + c) + ( b + d)i

18. Divide moduli and subtract arguments
irrational
i²
(cos? +isin?)n
Polar Coordinates - Division

19. No i
0 if and only if a = b = 0
How to solve (2i+3)/(9-i)
real
ln z

20. A subset within a field.
the vector (a -b)
Complex Addition
cos iy
Subfield

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.
Euler's Formula
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
i^0
Complex numbers are points in the plane

22. For real a and b - a + bi =
z1 / z2
0 if and only if a = b = 0
v(-1)
Polar Coordinates - z?¹

23. 1st. Rule of Complex Arithmetic
i^2 = -1
imaginary
complex
i^2

24. Where the curvature of the graph changes
Complex Number
Integers
point of inflection
Affix

25. Every complex number has the 'Standard Form':
a real number: (a + bi)(a - bi) = a² + b²
a + bi for some real a and b.
Complex Addition
Irrational Number

26. ? = -tan?
Liouville's Theorem -
Polar Coordinates - Arg(z*)
natural
Complex Number Formula

27. A complex number may be taken to the power of another complex number.
How to solve (2i+3)/(9-i)
Argand diagram
Complex Exponentiation
e^(ln z)

28. Rotates anticlockwise by p/2
a real number: (a + bi)(a - bi) = a² + b²
Polar Coordinates - Multiplication by i
z1 ^ (z2)
interchangeable

29. Have radical
z1 / z2
Complex Addition
can't get out of the complex numbers by adding (or subtracting) or multiplying two
radicals

30. Given (4-2i) the complex conjugate would be (4+2i)
complex
x-axis in the complex plane
the vector (a -b)
Complex Conjugate

31. 2a
Square Root
Euler Formula
has a solution.
z + z*

32. Not on the numberline
Field
(a + c) + ( b + d)i
non-integers
natural

33. Written as fractions - terminating + repeating decimals
Rules of Complex Arithmetic
radicals
rational
zz*

34. (a + bi) = (c + bi) =
Argand diagram
interchangeable
multiplying complex numbers
(a + c) + ( b + d)i

35. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
|z| = mod(z)
sin iy
the distance from z to the origin in the complex plane
Roots of Unity

36. 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
multiply the numerator and the denominator by the complex conjugate of the denominator.
Complex Addition
Rational Number
Complex Numbers: Add & subtract

37. I
v(-1)
i^4
standard form of complex numbers
|z-w|

38. V(x² + y²) = |z|
sin z
Subfield
Polar Coordinates - r
Complex Multiplication

39. ½(e^(-y) +e^(y)) = cosh y
Complex Number Formula
cos iy
The Complex Numbers
Polar Coordinates - Arg(z*)

40. Numbers on a numberline
integers
Complex Numbers: Multiply
imaginary
|z-w|

41. When two complex numbers are divided.
sin z
Complex Division
The Complex Numbers
a real number: (a + bi)(a - bi) = a² + b²

42. 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
Euler's Formula
sin iy
adding complex numbers
sin z

43. To simplify the square root of a negative number
multiplying complex numbers
|z| = mod(z)
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Rules of Complex Arithmetic

44. 1
Real and Imaginary Parts
i^2
standard form of complex numbers
four different numbers: i - -i - 1 - and -1.

45. 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
Complex Exponentiation
|z-w|
subtracting complex numbers
the complex numbers

46. Like pi
How to multiply complex nubers(2+i)(2i-3)
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
rational
transcendental

47. Starts at 1 - does not include 0
Complex Subtraction
x-axis in the complex plane
Integers
natural

48. A² + b² - real and non negative
Complex Conjugate
zz*
How to multiply complex nubers(2+i)(2i-3)
Polar Coordinates - Arg(z*)

49. The field of all rational and irrational numbers.
Roots of Unity
Real Numbers
sin z
conjugate pairs

50. A + bi
standard form of complex numbers
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
complex
(a + c) + ( b + d)i