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. For real a and b - a + bi =
Any polynomial O(xn) - (n > 0)
0 if and only if a = b = 0
imaginary
|z| = mod(z)

2. 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.
sin iy
How to multiply complex nubers(2+i)(2i-3)
Complex Numbers: Multiply
For real a and b - a + bi = 0 if and only if a = b = 0

3. Root negative - has letter i
adding complex numbers
imaginary
cos iy
Imaginary number

4. E^(ln r) e^(i?) e^(2pin)
transcendental
e^(ln z)
Integers
Polar Coordinates - z

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. A² + b² - real and non negative
zz*
Complex Number
Polar Coordinates - z?¹
Complex Exponentiation

7. A complex number may be taken to the power of another complex number.
real
Complex Exponentiation
How to add and subtract complex numbers (2-3i)-(4+6i)
The Complex Numbers

8. All the powers of i can be written as
The Complex Numbers
Euler's Formula
can't get out of the complex numbers by adding (or subtracting) or multiplying two
four different numbers: i - -i - 1 - and -1.

9. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
How to find any Power
transcendental
Integers
the distance from z to the origin in the complex plane

10. A + bi
Polar Coordinates - Multiplication by i
standard form of complex numbers
ln z
imaginary

11. All numbers
the distance from z to the origin in the complex plane
complex
four different numbers: i - -i - 1 - and -1.
Polar Coordinates - r

12. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
How to solve (2i+3)/(9-i)
Complex Division
multiplying complex numbers
|z| = mod(z)

13. ½(e^(-y) +e^(y)) = cosh y
Euler's Formula
The Complex Numbers
cos iy
Rules of Complex Arithmetic

14. Every complex number has the 'Standard Form':
z - z*
standard form of complex numbers
complex
a + bi for some real a and b.

15. 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
z1 / z2
Imaginary number
multiply the numerator and the denominator by the complex conjugate of the denominator.

16. 2ib
z - z*
Polar Coordinates - cos?
integers
Real Numbers

17. Divide moduli and subtract arguments
z - z*
Polar Coordinates - Division
a real number: (a + bi)(a - bi) = a² + b²
Field

18. Has exactly n roots by the fundamental theorem of algebra
Any polynomial O(xn) - (n > 0)
0 if and only if a = b = 0
integers
conjugate pairs

19. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
subtracting complex numbers
Absolute Value of a Complex Number
rational
z1 ^ (z2)

20. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Roots of Unity
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Complex Exponentiation
Real Numbers

21. R^2 = x
cosh²y - sinh²y
z + z*
Square Root
Complex Numbers: Add & subtract

22. A number that can be expressed as a fraction p/q where q is not equal to 0.
How to find any Power
Rational Number
i^4
Polar Coordinates - cos?

23. Imaginary number

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

24. (e^(-y) - e^(y)) / 2i = i sinh y
sin iy
Square Root
We say that c+di and c-di are complex conjugates.
cos iy

25. 4th. Rule of Complex Arithmetic
For real a and b - a + bi = 0 if and only if a = b = 0
(a + bi) = (c + bi) = (a + c) + ( b + d)i
x-axis in the complex plane
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

26. The square root of -1.
Imaginary Unit
transcendental
Complex Addition
Complex Number Formula

27. Like pi
complex
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
i²
transcendental

28. 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

29. 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
the complex numbers
subtracting complex numbers
Affix
(cos? +isin?)n

30. 5th. Rule of Complex Arithmetic
natural
De Moivre's Theorem
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
How to find any Power

31. Starts at 1 - does not include 0
can't get out of the complex numbers by adding (or subtracting) or multiplying two
natural
Absolute Value of a Complex Number
the complex numbers

32. Real and imaginary numbers
(a + bi) = (c + bi) = (a + c) + ( b + d)i
complex numbers
adding complex numbers
ln z

33. Where the curvature of the graph changes
point of inflection
(a + c) + ( b + d)i
Real and Imaginary Parts
Rules of Complex Arithmetic

34. Multiply moduli and add arguments
cos z
Polar Coordinates - Multiplication
adding complex numbers
Every complex number has the 'Standard Form': a + bi for some real a and b.

35. 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
cos z
Complex numbers are points in the plane
The Complex Numbers
Complex Numbers: Add & subtract

36. A+bi
How to multiply complex nubers(2+i)(2i-3)
conjugate
Complex Number Formula
standard form of complex numbers

37. The reals are just the
rational
conjugate pairs
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
x-axis in the complex plane

38. Any number not rational
Irrational Number
irrational
cos z
real

39. The complex number z representing a+bi.
Polar Coordinates - Division
Affix
complex
Imaginary Numbers

40. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called
Field
The Complex Numbers
x-axis in the complex plane
Polar Coordinates - z?¹

41. ½(e^(iz) + e^(-iz))
imaginary
the complex numbers
cos z
Any polynomial O(xn) - (n > 0)

42. z1z2* / |z2|²
The Complex Numbers
z1 / z2
conjugate
i^2 = -1

43. A subset within a field.
Subfield
the complex numbers
Complex Numbers: Multiply
Complex Addition

44. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
Complex Multiplication
ln z
Absolute Value of a Complex Number
i^2 = -1

45. A plot of complex numbers as points.
How to add and subtract complex numbers (2-3i)-(4+6i)
Complex Conjugate
radicals
Argand diagram

46. 2a
z + z*
Rules of Complex Arithmetic
-1
ln z

47. (e^(iz) - e^(-iz)) / 2i
(a + c) + ( b + d)i
v(-1)
sin z
i^2

48. Derives z = a+bi
How to add and subtract complex numbers (2-3i)-(4+6i)
sin iy
Euler Formula
the distance from z to the origin in the complex plane

49. 2nd. Rule of Complex Arithmetic

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

50. (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
Rules of Complex Arithmetic
sin iy
Euler's Formula
How to multiply complex nubers(2+i)(2i-3)