SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
Test your basic knowledge |
CLEP General Mathematics: Complex Numbers
Start Test
Study First
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. y / r
Polar Coordinates - sin?
Complex Subtraction
integers
i^0
2. Root negative - has letter i
e^(ln z)
imaginary
cos z
Integers
3. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i
How to add and subtract complex numbers (2-3i)-(4+6i)
Polar Coordinates - Multiplication
(cos? +isin?)n
a real number: (a + bi)(a - bi) = a² + b²
4. I
i^1
radicals
|z| = mod(z)
Polar Coordinates - Arg(z*)
5. Every complex number has the 'Standard Form':
z - z*
multiplying complex numbers
|z| = mod(z)
a + bi for some real a and b.
6. 3
real
i^3
Roots of Unity
Complex Exponentiation
7. 2nd. Rule of Complex Arithmetic
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
8. Written as fractions - terminating + repeating decimals
rational
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Complex numbers are points in the plane
Polar Coordinates - sin?
9. All the powers of i can be written as
four different numbers: i - -i - 1 - and -1.
conjugate pairs
How to find any Power
adding complex numbers
10. 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
11. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Roots of Unity
Integers
complex
sin z
12. E^(ln r) e^(i?) e^(2pin)
Rational Number
e^(ln z)
Every complex number has the 'Standard Form': a + bi for some real a and b.
Complex Subtraction
13. Multiply moduli and add arguments
Subfield
the distance from z to the origin in the complex plane
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
Polar Coordinates - Multiplication
14. R^2 = x
radicals
Imaginary Numbers
transcendental
Square Root
15. 4th. Rule of Complex Arithmetic
(a + bi) = (c + bi) = (a + c) + ( b + d)i
Liouville's Theorem -
complex
interchangeable
16. 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
Imaginary Numbers
i²
Polar Coordinates - Division
17. x + iy = r(cos? + isin?) = re^(i?)
Polar Coordinates - z
ln z
z1 ^ (z2)
transcendental
18. 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
Imaginary number
subtracting complex numbers
Irrational Number
19. 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
transcendental
Complex Numbers: Add & subtract
non-integers
adding complex numbers
20. Cos n? + i sin n? (for all n integers)
Complex Number
Imaginary number
(cos? +isin?)n
z - z*
21. 1
has a solution.
i^0
Square Root
multiplying complex numbers
22. (a + bi)(c + bi) =
How to find any Power
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
Euler's Formula
Irrational Number
23. 1
sin iy
Polar Coordinates - cos?
imaginary
i²
24. The field of all rational and irrational numbers.
Real Numbers
natural
Rules of Complex Arithmetic
How to multiply complex nubers(2+i)(2i-3)
25. xpressions such as ``the complex number z'' - and ``the point z'' are now
interchangeable
the vector (a -b)
i^3
i^2 = -1
26. 3rd. Rule of Complex Arithmetic
i^1
For real a and b - a + bi = 0 if and only if a = b = 0
i^3
transcendental
27. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
ln z
imaginary
sin z
cosh²y - sinh²y
28. Derives z = a+bi
Complex Subtraction
z1 ^ (z2)
Euler Formula
How to add and subtract complex numbers (2-3i)-(4+6i)
29. We see in this way that the distance between two points z and w in the complex plane is
Complex Addition
Imaginary Unit
|z-w|
Euler Formula
30. Starts at 1 - does not include 0
(a + bi) = (c + bi) = (a + c) + ( b + d)i
(a + c) + ( b + d)i
Every complex number has the 'Standard Form': a + bi for some real a and b.
natural
31. (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)
four different numbers: i - -i - 1 - and -1.
Square Root
Complex Subtraction
32. 1
i^2
Polar Coordinates - cos?
i^4
i²
33. When two complex numbers are subtracted from one another.
How to add and subtract complex numbers (2-3i)-(4+6i)
Complex Subtraction
Affix
i^1
34. x / r
natural
Polar Coordinates - cos?
How to multiply complex nubers(2+i)(2i-3)
real
35. 1st. Rule of Complex Arithmetic
i^2 = -1
z1 / z2
rational
irrational
36. 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
37. Like pi
cos iy
interchangeable
transcendental
The Complex Numbers
38. R?¹(cos? - isin?)
Complex Numbers: Add & subtract
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Polar Coordinates - z?¹
i^4
39. Given (4-2i) the complex conjugate would be (4+2i)
Real and Imaginary Parts
-1
transcendental
Complex Conjugate
40. 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.'
Absolute Value of a Complex Number
multiply the numerator and the denominator by the complex conjugate of the denominator.
Complex Number
Polar Coordinates - Arg(z*)
41. ½(e^(iz) + e^(-iz))
rational
cos z
Polar Coordinates - z?¹
Real and Imaginary Parts
42. 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 Subtraction
Complex Multiplication
Complex Addition
Complex Numbers: Add & subtract
43. 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
Any polynomial O(xn) - (n > 0)
Complex Numbers: Add & subtract
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
subtracting complex numbers
44. I
the complex numbers
v(-1)
conjugate pairs
can't get out of the complex numbers by adding (or subtracting) or multiplying two
45. The square root of -1.
Imaginary Numbers
Imaginary Unit
(a + c) + ( b + d)i
Euler Formula
46. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
z1 ^ (z2)
multiplying complex numbers
0 if and only if a = b = 0
Square Root
47. When two complex numbers are multipiled together.
conjugate pairs
Complex Multiplication
Imaginary Unit
z1 / z2
48. A number that cannot be expressed as a fraction for any integer.
conjugate
Irrational Number
Rational Number
ln z
49. Any number not rational
natural
transcendental
irrational
multiplying complex numbers
50. The complex number z representing a+bi.
has a solution.
z - z*
can't get out of the complex numbers by adding (or subtracting) or multiplying two
Affix