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
Polar Coordinates - Multiplication
radicals
Complex Division
Polar Coordinates - Multiplication by i

2. We can also think of the point z= a+ ib as
radicals
complex
the vector (a -b)
rational

3. 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.
rational
|z| = mod(z)
Complex Number Formula
How to find any Power

4. To simplify the square root of a negative number
complex numbers
z - z*
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
irrational

5. When two complex numbers are subtracted from one another.
rational
point of inflection
four different numbers: i - -i - 1 - and -1.
Complex Subtraction

6. 2nd. Rule of Complex Arithmetic

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

7. x / r
Polar Coordinates - cos?
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
z1 ^ (z2)
the vector (a -b)

8. E^(ln r) e^(i?) e^(2pin)
e^(ln z)
z + z*
the vector (a -b)
|z| = mod(z)

9. A complex number may be taken to the power of another complex number.
Complex Exponentiation
Real and Imaginary Parts
conjugate
i^3

10. Numbers on a numberline
integers
cos z
Complex Number Formula
Complex Conjugate

11. The complex number z representing a+bi.
Complex Division
Liouville's Theorem -
Affix
How to find any Power

12. The product of an imaginary number and its conjugate is
i^3
natural
a real number: (a + bi)(a - bi) = a² + b²
Complex Division

13. (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
'i'
How to solve (2i+3)/(9-i)
How to multiply complex nubers(2+i)(2i-3)
z1 / z2

14. 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 Number
(a + c) + ( b + d)i
Field
Complex Numbers: Multiply

15. 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
Square Root
adding complex numbers
Complex Subtraction
Complex Numbers: Add & subtract

16. I^2 =
-1
zz*
De Moivre's Theorem
Complex Conjugate

17. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Complex Numbers: Add & subtract
ln z
Euler's Formula

18. 4th. Rule of Complex Arithmetic
i^2
Every complex number has the 'Standard Form': a + bi for some real a and b.
z1 / z2
(a + bi) = (c + bi) = (a + c) + ( b + d)i

19. 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

20. V(x² + y²) = |z|
imaginary
'i'
Rules of Complex Arithmetic
Polar Coordinates - r

21. Have radical
radicals
can't get out of the complex numbers by adding (or subtracting) or multiplying two
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
a + bi for some real a and b.

22. To simplify a complex fraction
multiply the numerator and the denominator by the complex conjugate of the denominator.
ln z
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
four different numbers: i - -i - 1 - and -1.

23. Starts at 1 - does not include 0
Euler's Formula
rational
natural
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

24. Every complex number has the 'Standard Form':
Liouville's Theorem -
non-integers
Polar Coordinates - z?¹
a + bi for some real a and b.

25. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
Irrational Number
conjugate
v(-1)
point of inflection

26. 1
natural
i^2
Complex Numbers: Multiply
irrational

27. When two complex numbers are added together.
Affix
z - z*
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Addition

28. Root negative - has letter i
v(-1)
How to multiply complex nubers(2+i)(2i-3)
imaginary
Absolute Value of a Complex Number

29. 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

30. Given (4-2i) the complex conjugate would be (4+2i)
z + z*
Complex Conjugate
Complex Numbers: Multiply
Imaginary Numbers

31. 3
i^3
standard form of complex numbers
subtracting complex numbers
e^(ln z)

32. ½(e^(iz) + e^(-iz))
x-axis in the complex plane
Rules of Complex Arithmetic
cos z
Polar Coordinates - Multiplication

33. A + bi
real
Polar Coordinates - sin?
Euler's Formula
standard form of complex numbers

34. 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
adding complex numbers
Imaginary Unit
conjugate pairs

35. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Polar Coordinates - r
(cos? +isin?)n
Absolute Value of a Complex Number
Roots of Unity

36. x + iy = r(cos? + isin?) = re^(i?)
conjugate
Polar Coordinates - z
For real a and b - a + bi = 0 if and only if a = b = 0
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

37. A subset within a field.
We say that c+di and c-di are complex conjugates.
point of inflection
Subfield
Complex Number Formula

38. 1
Euler's Formula
cosh²y - sinh²y
i^2
Complex Subtraction

39. xpressions such as ``the complex number z'' - and ``the point z'' are now
interchangeable
Polar Coordinates - Division
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
integers

40. The modulus of the complex number z= a + ib now can be interpreted as
Imaginary Numbers
i^4
the distance from z to the origin in the complex plane
|z| = mod(z)

41. A² + b² - real and non negative
four different numbers: i - -i - 1 - and -1.
(a + c) + ( b + d)i
zz*
interchangeable

42. When two complex numbers are multipiled together.
-1
Polar Coordinates - Multiplication
Polar Coordinates - z?¹
Complex Multiplication

43. Cos n? + i sin n? (for all n integers)
Roots of Unity
Any polynomial O(xn) - (n > 0)
(cos? +isin?)n
Polar Coordinates - Division

44. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
0 if and only if a = b = 0
x-axis in the complex plane
How to add and subtract complex numbers (2-3i)-(4+6i)
Imaginary number

45. A plot of complex numbers as points.
i^0
non-integers
Argand diagram
point of inflection

46. R?¹(cos? - isin?)
Complex Conjugate
cosh²y - sinh²y
conjugate
Polar Coordinates - z?¹

47. Real and imaginary numbers
multiply the numerator and the denominator by the complex conjugate of the denominator.
Rules of Complex Arithmetic
Euler's Formula
complex numbers

48. The square root of -1.
z + z*
Imaginary Unit
Complex Division
'i'

49. 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 Numbers: Multiply
Complex Number
i²
'i'

50. 3rd. Rule of Complex Arithmetic
Polar Coordinates - z
For real a and b - a + bi = 0 if and only if a = b = 0
multiplying complex numbers
Real and Imaginary Parts