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. 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
Complex Numbers: Add & subtract
How to multiply complex nubers(2+i)(2i-3)
Complex Number Formula
radicals

2. Cos n? + i sin n? (for all n integers)
cosh²y - sinh²y
(cos? +isin?)n
Polar Coordinates - sin?
zz*

3. 2ib
z1 ^ (z2)
cos iy
z - z*
z1 / z2

4. A+bi
Complex Number Formula
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Polar Coordinates - Division
Polar Coordinates - cos?

5. To simplify a complex fraction
adding complex numbers
multiply the numerator and the denominator by the complex conjugate of the denominator.
the vector (a -b)
i^1

6. 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 - sin?
sin z
How to solve (2i+3)/(9-i)
the complex numbers

7. All the powers of i can be written as
z1 ^ (z2)
non-integers
Rational Number
four different numbers: i - -i - 1 - and -1.

8. A number that cannot be expressed as a fraction for any integer.
ln z
Irrational Number
Polar Coordinates - cos?
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

9. When two complex numbers are subtracted from one another.
Imaginary Unit
rational
conjugate pairs
Complex Subtraction

10. Have radical
Complex Numbers: Multiply
e^(ln z)
radicals
i^3

11. A subset within a field.
rational
Subfield
Complex Exponentiation
z + z*

12. (a + bi)(c + bi) =
Polar Coordinates - z?¹
radicals
non-integers
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

13. 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
ln z
Polar Coordinates - r
Rational Number
adding complex numbers

14. z1z2* / |z2|²
non-integers
z1 / z2
i^3
Complex Number

15. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
0 if and only if a = b = 0
Field
z + z*
can't get out of the complex numbers by adding (or subtracting) or multiplying two

16. 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

17. Has exactly n roots by the fundamental theorem of algebra
Any polynomial O(xn) - (n > 0)
For real a and b - a + bi = 0 if and only if a = b = 0
Complex Addition
-1

18. 1
i^2
Affix
Polar Coordinates - z
Imaginary number

19. 1
Rational Number
Complex Subtraction
i²
Affix

20. When two complex numbers are divided.
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Complex Division
How to add and subtract complex numbers (2-3i)-(4+6i)
multiply the numerator and the denominator by the complex conjugate of the denominator.

21. (e^(-y) - e^(y)) / 2i = i sinh y
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Polar Coordinates - r
sin iy
Affix

22. A² + b² - real and non negative
z1 ^ (z2)
adding complex numbers
Polar Coordinates - r
zz*

23. Not on the numberline
Imaginary Unit
sin iy
non-integers
Complex Subtraction

24. 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

25. 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.'
Imaginary Numbers
Complex Number
i^2
i^3

26. (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)
Euler Formula
Complex Division
Polar Coordinates - sin?

27. 1
non-integers
i^0
Rules of Complex Arithmetic
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i

28. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
cos iy
sin z
0 if and only if a = b = 0
ln z

29. E^(ln r) e^(i?) e^(2pin)
e^(ln z)
Polar Coordinates - sin?
Complex Division
'i'

30. Rotates anticlockwise by p/2
Complex Numbers: Add & subtract
Polar Coordinates - Multiplication by i
'i'
Complex numbers are points in the plane

31. The complex number z representing a+bi.
(cos? +isin?)n
Affix
Rules of Complex Arithmetic
rational

32. Derives z = a+bi
conjugate
Complex Subtraction
Real Numbers
Euler Formula

33. ½(e^(iz) + e^(-iz))
cos z
'i'
(a + bi) = (c + bi) = (a + c) + ( b + d)i
complex

34. Imaginary number

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

35. When two complex numbers are added together.
Complex Conjugate
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Complex Addition
Absolute Value of a Complex Number

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. 1st. Rule of Complex Arithmetic
i^2
sin z
z - z*
i^2 = -1

38. 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.
v(-1)
multiplying complex numbers
Euler's Formula

39. A complex number may be taken to the power of another complex number.
Complex Exponentiation
Liouville's Theorem -
has a solution.
Polar Coordinates - z?¹

40. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called
Polar Coordinates - Multiplication by i
The Complex Numbers
Roots of Unity
point of inflection

41. 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
Square Root
Polar Coordinates - Arg(z*)
Rules of Complex Arithmetic
Complex Addition

42. The product of an imaginary number and its conjugate is
transcendental
Complex Numbers: Multiply
a real number: (a + bi)(a - bi) = a² + b²
i²

43. All numbers
Complex Conjugate
complex
Complex Addition
imaginary

44. The reals are just the
|z-w|
(a + c) + ( b + d)i
x-axis in the complex plane
Imaginary Unit

45. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Polar Coordinates - Division
conjugate
How to add and subtract complex numbers (2-3i)-(4+6i)

46. 3
i^3
Any polynomial O(xn) - (n > 0)
We say that c+di and c-di are complex conjugates.
v(-1)

47. 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.
the distance from z to the origin in the complex plane
Complex numbers are points in the plane
x-axis in the complex plane
Affix

48. V(zz*) = v(a² + b²)
|z| = mod(z)
Complex Numbers: Add & subtract
(a + bi) = (c + bi) = (a + c) + ( b + d)i
sin iy

49. x / r
z + z*
ln z
Polar Coordinates - cos?
point of inflection

50. R^2 = x
i^3
Square Root
radicals
Absolute Value of a Complex Number