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. I
Complex Number
How to add and subtract complex numbers (2-3i)-(4+6i)
Polar Coordinates - Multiplication
i^1
2. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.
How to add and subtract complex numbers (2-3i)-(4+6i)
i^4
Rational Number
Absolute Value of a Complex Number
3. 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
z - z*
adding complex numbers
complex numbers
Rules of Complex Arithmetic
4. Imaginary number
Warning
: Invalid argument supplied for foreach() in
/var/www/html/basicversity.com/show_quiz.php
on line
183
5. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n
Euler's Formula
z + z*
ln z
i^3
6. Starts at 1 - does not include 0
integers
Rational Number
natural
the distance from z to the origin in the complex plane
7. Root negative - has letter i
'i'
How to solve (2i+3)/(9-i)
imaginary
Roots of Unity
8. In this amazing number field every algebraic equation in z with complex coefficients
Complex Division
has a solution.
Every complex number has the 'Standard Form': a + bi for some real a and b.
Complex numbers are points in the plane
9. I = imaginary unit - i² = -1 or i = v-1
a + bi for some real a and b.
z + z*
Imaginary Numbers
i^1
10. E^(ln r) e^(i?) e^(2pin)
e^(ln z)
subtracting complex numbers
conjugate pairs
Polar Coordinates - cos?
11. V(zz*) = v(a² + b²)
Rules of Complex Arithmetic
|z| = mod(z)
Roots of Unity
x-axis in the complex plane
12. 2ib
i^0
i²
z - z*
cos z
13. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi
Complex Numbers: Multiply
Complex Division
transcendental
conjugate
14. (e^(-y) - e^(y)) / 2i = i sinh y
i^2 = -1
sin iy
Rules of Complex Arithmetic
z1 ^ (z2)
15. (a + bi)(c + bi) =
integers
ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
multiply the numerator and the denominator by the complex conjugate of the denominator.
i^2
16. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
irrational
(a + bi) = (c + bi) = (a + c) + ( b + d)i
multiplying complex numbers
i^1
17. 1
i^4
integers
Complex Numbers: Multiply
i^2 = -1
18. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called
four different numbers: i - -i - 1 - and -1.
The Complex Numbers
Complex Division
natural
19. We see in this way that the distance between two points z and w in the complex plane is
|z-w|
How to solve (2i+3)/(9-i)
(cos? +isin?)n
i^1
20. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.
Complex Numbers: Multiply
x-axis in the complex plane
Field
z - z*
21. We can also think of the point z= a+ ib as
zz*
the vector (a -b)
standard form of complex numbers
Euler's Formula
22. Written as fractions - terminating + repeating decimals
rational
Real and Imaginary Parts
'i'
Polar Coordinates - sin?
23. x / r
(a + c) + ( b + d)i
Polar Coordinates - cos?
transcendental
the complex numbers
24. 1
Rules of Complex Arithmetic
cos z
i^2
irrational
25. Where the curvature of the graph changes
Affix
point of inflection
irrational
Polar Coordinates - Multiplication by i
26. 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
Real and Imaginary Parts
i²
Polar Coordinates - Multiplication
|z-w|
27. A complex number may be taken to the power of another complex number.
Complex Number Formula
Complex Exponentiation
i^0
Euler Formula
28. Cos n? + i sin n? (for all n integers)
Complex Subtraction
'i'
(cos? +isin?)n
x-axis in the complex plane
29. Divide moduli and subtract arguments
Polar Coordinates - Division
a real number: (a + bi)(a - bi) = a² + b²
z1 / z2
'i'
30. The product of an imaginary number and its conjugate is
Polar Coordinates - Arg(z*)
Integers
a real number: (a + bi)(a - bi) = a² + b²
Real Numbers
31. The modulus of the complex number z= a + ib now can be interpreted as
Complex Division
sin z
the distance from z to the origin in the complex plane
Integers
32. xpressions such as ``the complex number z'' - and ``the point z'' are now
Liouville's Theorem -
has a solution.
the distance from z to the origin in the complex plane
interchangeable
33. 1
Affix
i^0
subtracting complex numbers
conjugate
34. (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
0 if and only if a = b = 0
x-axis in the complex plane
How to solve (2i+3)/(9-i)
Imaginary number
35. ½(e^(-y) +e^(y)) = cosh y
Real and Imaginary Parts
cos iy
Any polynomial O(xn) - (n > 0)
e^(ln z)
36. E ^ (z2 ln z1)
z1 ^ (z2)
Polar Coordinates - z?¹
Complex Multiplication
How to multiply complex nubers(2+i)(2i-3)
37. A complex number and its conjugate
conjugate
Polar Coordinates - cos?
Integers
conjugate pairs
38. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1
Roots of Unity
(a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc) + (bc + ad)i
rational
Polar Coordinates - sin?
39. Not on the numberline
Complex Exponentiation
you write the square root as the product of square roots and simplify: v(-a) = v(-1)v(a) = iv(a)
non-integers
sin iy
40. (a + bi) = (c + bi) =
complex
(cos? +isin?)n
-1
(a + c) + ( b + d)i
41. A number that can be expressed as a fraction p/q where q is not equal to 0.
natural
zz*
How to solve (2i+3)/(9-i)
Rational Number
42. 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
43. All the powers of i can be written as
i^2
Complex numbers are points in the plane
four different numbers: i - -i - 1 - and -1.
How to multiply complex nubers(2+i)(2i-3)
44. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....
four different numbers: i - -i - 1 - and -1.
v(-1)
Integers
Euler's Formula
45. V(x² + y²) = |z|
a + bi for some real a and b.
(cos? +isin?)n
Polar Coordinates - r
For real a and b - a + bi = 0 if and only if a = b = 0
46. 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
Complex Addition
Liouville's Theorem -
Polar Coordinates - z?¹
47. 1
i²
Complex Exponentiation
How to add and subtract complex numbers (2-3i)-(4+6i)
How to multiply complex nubers(2+i)(2i-3)
48. No i
interchangeable
Polar Coordinates - z?¹
real
Polar Coordinates - cos?
49. (e^(iz) - e^(-iz)) / 2i
sin z
Any polynomial O(xn) - (n > 0)
Liouville's Theorem -
Complex Numbers: Add & subtract
50. When two complex numbers are subtracted from one another.
Complex Subtraction
How to find any Power
ln z
Polar Coordinates - Multiplication by i