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. (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
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
How to multiply complex nubers(2+i)(2i-3)
Complex Numbers: Add & subtract
0 if and only if a = b = 0

2. (a + bi) = (c + bi) =
Imaginary Numbers
How to add and subtract complex numbers (2-3i)-(4+6i)
De Moivre's Theorem
(a + c) + ( b + d)i

3. I
i^1
multiplying complex numbers
rational
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)

4. E ^ (z2 ln z1)
Imaginary number
z1 ^ (z2)
How to solve (2i+3)/(9-i)
imaginary

5. 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.
i^1
i^4
the complex numbers
Complex numbers are points in the plane

6. A subset within a field.
v(-1)
Subfield
Imaginary Numbers
We say that c+di and c-di are complex conjugates.

7. Numbers on a numberline
Complex Exponentiation
complex
integers
How to multiply complex nubers(2+i)(2i-3)

8. A complex number may be taken to the power of another complex number.
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Real and Imaginary Parts
Complex Exponentiation
Real Numbers

9. 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
irrational
subtracting complex numbers
sin iy
Complex Number

10. Equivalent to an Imaginary Unit.
Imaginary number
cos iy
standard form of complex numbers
0 if and only if a = b = 0

11. 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
Polar Coordinates - cos?
Euler's Formula
i^0
We say that c+di and c-di are complex conjugates.

12. 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
(cos? +isin?)n
i^3
radicals
adding complex numbers

13. Have radical
How to multiply complex nubers(2+i)(2i-3)
radicals
Roots of Unity
Complex Number

14. All numbers
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Real Numbers
Polar Coordinates - z?¹
complex

15. 2nd. Rule of Complex Arithmetic

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

16. When two complex numbers are added together.
Complex Addition
the complex numbers
Subfield
|z| = mod(z)

17. Multiply moduli and add arguments
Integers
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - Multiplication
radicals

18. A + bi
z1 / z2
How to multiply complex nubers(2+i)(2i-3)
standard form of complex numbers
four different numbers: i - -i - 1 - and -1.

19. For real a and b - a + bi =
point of inflection
0 if and only if a = b = 0
Complex Multiplication
a real number: (a + bi)(a - bi) = a² + b²

20. 3rd. Rule of Complex Arithmetic
Complex Number
i^2
Real and Imaginary Parts
For real a and b - a + bi = 0 if and only if a = b = 0

21. To simplify the square root of a negative number
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Euler Formula
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
cos z

22. I
four different numbers: i - -i - 1 - and -1.
v(-1)
'i'
sin z

23. We see in this way that the distance between two points z and w in the complex plane is
Complex Number Formula
non-integers
|z-w|
conjugate pairs

24. When two complex numbers are subtracted from one another.
Complex Subtraction
i²
cos iy
radicals

25. Root negative - has letter i
a + bi for some real a and b.
Absolute Value of a Complex Number
Euler Formula
imaginary

26. Written as fractions - terminating + repeating decimals
adding complex numbers
rational
i^2
Complex Addition

27. 1
i^0
cos iy
standard form of complex numbers
i^4

28. Derives z = a+bi
imaginary
Euler Formula
i^2 = -1
standard form of complex numbers

29. I = imaginary unit - i² = -1 or i = v-1
Polar Coordinates - sin?
cos iy
Complex Division
Imaginary Numbers

30. 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 Numbers: Multiply
Rational Number
The Complex Numbers
Complex numbers are points in the plane

31. Not on the numberline
De Moivre's Theorem
non-integers
i^3
-1

32. 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
rational
Roots of Unity
Real and Imaginary Parts
point of inflection

33. Given (4-2i) the complex conjugate would be (4+2i)
Euler's Formula
Square Root
Complex Conjugate
For real a and b - a + bi = 0 if and only if a = b = 0

34. x / r
Polar Coordinates - cos?
the distance from z to the origin in the complex plane
the complex numbers
i^4

35. Any number not rational
v(-1)
i^4
Polar Coordinates - r
irrational

36. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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

37. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called
transcendental
Polar Coordinates - r
The Complex Numbers
For real a and b - a + bi = 0 if and only if a = b = 0

38. xpressions such as ``the complex number z'' - and ``the point z'' are now
interchangeable
four different numbers: i - -i - 1 - and -1.
the vector (a -b)
i^0

39. R?¹(cos? - isin?)
Polar Coordinates - z?¹
Euler Formula
natural
For real a and b - a + bi = 0 if and only if a = b = 0

40. ½(e^(-y) +e^(y)) = cosh y
cos z
Complex Numbers: Add & subtract
cos iy
radicals

41. We can also think of the point z= a+ ib as
Complex Division
the vector (a -b)
Complex Subtraction
How to find any Power

42. 4th. Rule of Complex Arithmetic
the vector (a -b)
Every complex number has the 'Standard Form': a + bi for some real a and b.
(a + bi) = (c + bi) = (a + c) + ( b + d)i
conjugate

43. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
Complex Subtraction
Rational Number
Absolute Value of a Complex Number
For real a and b - a + bi = 0 if and only if a = b = 0

44. When two complex numbers are multipiled together.
a real number: (a + bi)(a - bi) = a² + b²
Complex Multiplication
imaginary
Complex Numbers: Multiply

45. 1
We say that c+di and c-di are complex conjugates.
cosh²y - sinh²y
Complex numbers are points in the plane
the complex numbers

46. All the powers of i can be written as
cos z
four different numbers: i - -i - 1 - and -1.
Complex Numbers: Multiply
complex numbers

47. 2a
z + z*
rational
zz*
Imaginary number

48. R^2 = x
Square Root
complex
Polar Coordinates - Arg(z*)
De Moivre's Theorem

49. A² + b² - real and non negative
zz*
the complex numbers
Polar Coordinates - Multiplication
natural

50. To simplify a complex fraction
Polar Coordinates - z?¹
multiply the numerator and the denominator by the complex conjugate of the denominator.
point of inflection
interchangeable