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. Where the curvature of the graph changes
Square Root
point of inflection
the complex numbers
Affix

2. Have radical
Polar Coordinates - Arg(z*)
Polar Coordinates - z
radicals
cosh²y - sinh²y

3. 2a
i^1
Complex Addition
z + z*
Complex Exponentiation

4. 1
(cos? +isin?)n
Complex Exponentiation
i²
Polar Coordinates - Multiplication

5. 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

6. The square root of -1.
multiplying complex numbers
transcendental
natural
Imaginary Unit

7. We can also think of the point z= a+ ib as
the vector (a -b)
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Real and Imaginary Parts
Euler Formula

8. 2ib
point of inflection
Absolute Value of a Complex Number
z - z*
complex

9. I = imaginary unit - i² = -1 or i = v-1
zz*
Imaginary Numbers
Complex Numbers: Add & subtract
Polar Coordinates - sin?

10. A+bi
real
Complex Number Formula
Polar Coordinates - Arg(z*)
Complex Numbers: Add & subtract

11. Rotates anticlockwise by p/2
Polar Coordinates - Multiplication by i
sin iy
complex
Absolute Value of a Complex Number

12. A² + b² - real and non negative
Rules of Complex Arithmetic
Complex Addition
zz*
We say that c+di and c-di are complex conjugates.

13. The complex number z representing a+bi.
z - z*
adding complex numbers
Complex Number
Affix

14. A number that cannot be expressed as a fraction for any integer.
Liouville's Theorem -
Polar Coordinates - Arg(z*)
Irrational Number
Every complex number has the 'Standard Form': a + bi for some real a and b.

15. No i
has a solution.
real
conjugate
For real a and b - a + bi = 0 if and only if a = b = 0

16. 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 add and subtract complex numbers (2-3i)-(4+6i)
sin z
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
multiplying complex numbers

17. Starts at 1 - does not include 0
irrational
Complex numbers are points in the plane
Any polynomial O(xn) - (n > 0)
natural

18. xpressions such as ``the complex number z'' - and ``the point z'' are now
z1 / z2
i^4
interchangeable
For real a and b - a + bi = 0 if and only if a = b = 0

19. Written as fractions - terminating + repeating decimals
Complex Subtraction
rational
We say that c+di and c-di are complex conjugates.
the distance from z to the origin in the complex plane

20. The product of an imaginary number and its conjugate is
Irrational Number
0 if and only if a = b = 0
a real number: (a + bi)(a - bi) = a² + b²
The Complex Numbers

21. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Subfield
Absolute Value of a Complex Number
Any polynomial O(xn) - (n > 0)
0 if and only if a = b = 0

22. (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
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Roots of Unity
How to solve (2i+3)/(9-i)
i^2

23. ? = -tan?
Polar Coordinates - Arg(z*)
a real number: (a + bi)(a - bi) = a² + b²
i²
Argand diagram

24. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Complex Division
Roots of Unity
Argand diagram
|z-w|

25. 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

26. 4th. Rule of Complex Arithmetic
(a + bi) = (c + bi) = (a + c) + ( b + d)i
z + z*
Absolute Value of a Complex Number
0 if and only if a = b = 0

27. 1
'i'
natural
|z| = mod(z)
i^2

28. z1z2* / |z2|²
z1 / z2
De Moivre's Theorem
Liouville's Theorem -
Roots of Unity

29. R^2 = x
conjugate
For real a and b - a + bi = 0 if and only if a = b = 0
Polar Coordinates - r
Square Root

30. In this amazing number field every algebraic equation in z with complex coefficients
has a solution.
Euler Formula
Polar Coordinates - sin?
(a + c) + ( b + d)i

31. x / r
Polar Coordinates - cos?
'i'
We say that c+di and c-di are complex conjugates.
z + z*

32. To simplify the square root of a negative number
How to multiply complex nubers(2+i)(2i-3)
Polar Coordinates - Arg(z*)
i^0
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

33. y / r
The Complex Numbers
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Polar Coordinates - sin?
i^1

34. 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
the complex numbers
Complex Numbers: Add & subtract
0 if and only if a = b = 0
For real a and b - a + bi = 0 if and only if a = b = 0

35. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
Integers
|z| = mod(z)
How to add and subtract complex numbers (2-3i)-(4+6i)
rational

36. When two complex numbers are added together.
De Moivre's Theorem
Complex Addition
Imaginary number
irrational

37. Given (4-2i) the complex conjugate would be (4+2i)
How to find any Power
Complex Division
i^1
Complex Conjugate

38. 1
Polar Coordinates - sin?
the distance from z to the origin in the complex plane
real
cosh²y - sinh²y

39. 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
natural
Rules of Complex Arithmetic
transcendental
For real a and b - a + bi = 0 if and only if a = b = 0

40. Real and imaginary numbers
Complex Conjugate
i^3
complex numbers
real

41. (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
cosh²y - sinh²y
imaginary
|z-w|
How to multiply complex nubers(2+i)(2i-3)

42. All numbers
i^4
complex
subtracting complex numbers
the vector (a -b)

43. ½(e^(-y) +e^(y)) = cosh y
Any polynomial O(xn) - (n > 0)
a real number: (a + bi)(a - bi) = a² + b²
Complex Conjugate
cos iy

44. Equivalent to an Imaginary Unit.
Imaginary Numbers
conjugate pairs
Liouville's Theorem -
Imaginary number

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
interchangeable
|z| = mod(z)
Polar Coordinates - Division
subtracting complex numbers

46. Any number not rational
Any polynomial O(xn) - (n > 0)
Polar Coordinates - r
irrational
Real and Imaginary Parts

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
the complex numbers
a real number: (a + bi)(a - bi) = a² + b²
transcendental
four different numbers: i - -i - 1 - and -1.

48. 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.
Any polynomial O(xn) - (n > 0)
Complex Numbers: Multiply
Polar Coordinates - Arg(z*)
radicals

49. Like pi
transcendental
Liouville's Theorem -
Real and Imaginary Parts
Polar Coordinates - sin?

50. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that
We say that c+di and c-di are complex conjugates.
Polar Coordinates - r
Complex numbers are points in the plane
rational