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. Have radical
cosh²y - sinh²y
adding complex numbers
radicals
Real Numbers

2. x + iy = r(cos? + isin?) = re^(i?)
The Complex Numbers
Rational Number
z1 / z2
Polar Coordinates - z

3. A complex number and its conjugate
conjugate pairs
Complex Number
integers
Polar Coordinates - Multiplication

4. V(zz*) = v(a² + b²)
Polar Coordinates - Multiplication
|z| = mod(z)
Argand diagram
0 if and only if a = b = 0

5. Starts at 1 - does not include 0
natural
subtracting complex numbers
z1 / z2
How to solve (2i+3)/(9-i)

6. Equivalent to an Imaginary Unit.
Imaginary number
cos z
Any polynomial O(xn) - (n > 0)
i^4

7. When two complex numbers are divided.
z1 / z2
i^2
Complex Division
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

8. Every complex number has the 'Standard Form':
Real and Imaginary Parts
point of inflection
z1 ^ (z2)
a + bi for some real a and b.

9. Multiply moduli and add arguments
has a solution.
i^2
Argand diagram
Polar Coordinates - Multiplication

10. (a + bi)(c + bi) =
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
|z-w|
Euler's Formula
-1

11. 1
Polar Coordinates - Division
i^0
Field
zz*

12. The modulus of the complex number z= a + ib now can be interpreted as
the distance from z to the origin in the complex plane
Complex Numbers: Add & subtract
point of inflection
Polar Coordinates - r

13. 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

14. 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.
How to find any Power
i^2
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
(a + c) + ( b + d)i

15. ? = -tan?
Polar Coordinates - Arg(z*)
How to solve (2i+3)/(9-i)
Euler's Formula
Liouville's Theorem -

16. z1z2* / |z2|²
a + bi for some real a and b.
z1 / z2
Subfield
Field

17. Cos n? + i sin n? (for all n integers)
(cos? +isin?)n
Euler's Formula
Complex Number Formula
multiply the numerator and the denominator by the complex conjugate of the denominator.

18. ½(e^(-y) +e^(y)) = cosh y
Argand diagram
De Moivre's Theorem
i^0
cos iy

19. 2ib
Field
Polar Coordinates - Multiplication
Any polynomial O(xn) - (n > 0)
z - z*

20. Divide moduli and subtract arguments
Polar Coordinates - Division
Field
Imaginary Numbers
Polar Coordinates - cos?

21. 5th. Rule of Complex Arithmetic
Polar Coordinates - Division
i²
Absolute Value of a Complex Number
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

22. 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

23. A complex number may be taken to the power of another complex number.
Complex Exponentiation
Imaginary Unit
Complex Number Formula
v(-1)

24. 1
Any polynomial O(xn) - (n > 0)
(a + bi) = (c + bi) = (a + c) + ( b + d)i
i²
has a solution.

25. V(x² + y²) = |z|
complex numbers
Polar Coordinates - Multiplication by i
For real a and b - a + bi = 0 if and only if a = b = 0
Polar Coordinates - r

26. All the powers of i can be written as
natural
four different numbers: i - -i - 1 - and -1.
i^4
Complex Conjugate

27. For real a and b - a + bi =
x-axis in the complex plane
Absolute Value of a Complex Number
0 if and only if a = b = 0
natural

28. A plot of complex numbers as points.
imaginary
Argand diagram
Polar Coordinates - Arg(z*)
Any polynomial O(xn) - (n > 0)

29. The square root of -1.
|z| = mod(z)
non-integers
Imaginary Unit
transcendental

30. 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
Real and Imaginary Parts
Euler Formula
(a + bi) = (c + bi) = (a + c) + ( b + d)i
|z| = mod(z)

31. Root negative - has letter i
imaginary
Real and Imaginary Parts
Euler Formula
v(-1)

32. (e^(iz) - e^(-iz)) / 2i
For real a and b - a + bi = 0 if and only if a = b = 0
(a + c) + ( b + d)i
sin z
complex

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
How to solve (2i+3)/(9-i)
Polar Coordinates - Multiplication
Irrational Number
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

34. The reals are just the
x-axis in the complex plane
i^3
sin z
(cos? +isin?)n

35. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called
The Complex Numbers
subtracting complex numbers
i^2 = -1
Polar Coordinates - z?¹

36. When two complex numbers are added together.
standard form of complex numbers
cosh²y - sinh²y
Complex Addition
Polar Coordinates - Multiplication by i

37. Numbers on a numberline
z - z*
radicals
integers
Complex Number

38. 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

39. To simplify a complex fraction
Field
multiply the numerator and the denominator by the complex conjugate of the denominator.
Rational Number
Complex Numbers: Multiply

40. 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.
Complex Addition
the vector (a -b)
cos iy
Complex Numbers: Multiply

41. A + bi
z + z*
Imaginary Numbers
Complex Conjugate
standard form of complex numbers

42. The complex number z representing a+bi.
zz*
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Affix
Liouville's Theorem -

43. Imaginary number

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

44. I
Rules of Complex Arithmetic
Polar Coordinates - Multiplication by i
i^1
sin iy

45. 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
non-integers
cosh²y - sinh²y
imaginary
Complex Numbers: Add & subtract

46. Real and imaginary numbers
Square Root
Complex Conjugate
complex numbers
i^2

47. 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
Polar Coordinates - Arg(z*)
(a + bi) = (c + bi) = (a + c) + ( b + d)i
the complex numbers
rational

48. 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
subtracting complex numbers
Roots of Unity
i²
Complex numbers are points in the plane

49. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
Polar Coordinates - z?¹
multiply the numerator and the denominator by the complex conjugate of the denominator.
How to add and subtract complex numbers (2-3i)-(4+6i)
Integers

50. Given (4-2i) the complex conjugate would be (4+2i)
Polar Coordinates - z?¹
Complex Addition
Complex Conjugate
Rules of Complex Arithmetic