0
Complex Numbers
The square root of negative one, which we now call the imaginary unit, was once thought to be an absurd notion. However, through the diligent studies of open-minded mathematicians, it was shown that the real numbers were actually just one part of a larger set of numbers known as the complex numbers, the other part being the imaginary numbers. Please direct all questions about these surprisingly useful and applicable numbers into this category.
887 Questions
Can you divide infinity by an imaginary number?
Yes, but the answer will be in infinities within the complex domain. Unless you know what you are doing there, stay away ;)
What is a nonzero real number?
It's any real number distinct from 0.
For instance, in the expression x/y, where x and y are real numbers, y needs to be a nonzero real number. This is because otherwise the expression x/y is undefined (viz. x/0).
How do you find caste certificate number on internet?
Depending on where the Caste certificate was applied for and registered, is where one might start to look. One may obtain it over the net by contacting the same place they registered with.
Who first wrote about complex numbers?
The Italian mathematician, Gerolamo Cardano was the first to consider the concept of complex numbers. However, he did not develop a theory of complex numbers to any extent. That was left to Rafael Bombelli.
How do you use complex numbers?
Better get a textbook that explains this in more detail. You can also get a brief summary at Wikipedia, or other online sites.
In any case, here is a brief summary.
For addition and substraction, you add (or subtract) the real and imaginary parts separately. For example, (4 + 3i) + (7 - 2i) = 11 + 1.
For multiplication, multiply each part of one number with each part of the other number - and remember that i2 = -1. For example, (4 + 3i) x (7 - 2i) = 28 - 8i + 21i - 6i2 = 28 + 13i - 6(-1) = 34 + 13i.
Division is a bit more complicated. For example, to divide by (3 + 4i) you have to multiply numerator and denominator by the complex conjugate of this number, that is, change the sign of the imaginary part; in this case, (3 - 4i).
Multiplication and division are actually quite a lot easier if you convert the complex number to polar coordinates, that is, a distance and an angle. Here is a quick example: (4 angle 30 degrees) x (5 angle 20 degrees) = (4 x 5) angle (30 + 20 degrees) = 20 angle 50 degrees (a length of 20, at an angle of 50 degrees). Most scientific calculators have special functions to convert from rectangular to polar coordinates and back.
Which set of numbers does 9 belong to?
9 belongs in the sets:
-Natural number set, positive whole numbers
-Integer number set, whole numbers
-Rational number set, numbers that are not never ending
-Real number set, basic numbers without i and that can be expressed in say amounts of apples
-Complex number set, the set that contains both real and unreal numbers
What is the complex number of its distance for the origin in the complex plane?
This is called the magnitude. It can be found (for a complex number a + bi) as:
(where a & b are both real numbers and i is the imaginary unit)
sqrt(a^2 + b^2)
Find the fourth complex roots of w equals 81 and plot them?
if the question is w^4 = 81 {w raised to the power of 4},
Then the four roots are w = {3, -3, 3i, -3i}.
The plots on the real-imaginary plane would be the points:
- (3,0)
- (-3,0)
- (0,3)
- (0,-3)
The answer is Yes, for the purposes of most Math students. There are, number systems that have been devised which are outside the set of Complex Numbers, though.
What are the 3 undefined terms in geometry and their definition?
Points, lines & planes.
Point - a dot on a page. A point has no dimensions (length, width, height), it is usually represent by a capital letter and a dot on a page. Think of it as an infinitely small place or position on a map.
Line - an unlimited number of points along the same path. The set of points may be straight or form a curve. Normally, the term 'line' means a straight line. The 'line' has no dimensions (length, width, height) and extends unlimited in both directions. (The part of a line defined by two points, called 'endpoints', is call a line segment or 'segment'.) A 'line' is represented by a drawn line with arrowheads on each end to represent that it doesn't have endpoints. A line can be named in two ways: (1) use the capital letters representing two points on the line and place a double-headed arrow above the two letters (2) use a lowercase letter beside the line to represent it.
Plane - a flat surface that extends indefinitely in all directions. It is usually represented by a parallelogram (four sided figure) with a capital letter in one corner. Remember the plane is not limited by the parallelogram, it extends infinitely. The plane can also be represented by using three points that lie on the plane surface but not on the same line (noncollinear).
Do any of these sets have element in each common of real number?
It kind of depends on what "these" sets are.
If z equals a plus ib then show that arg conjugate of z equals 2pi -arg z?
If z = a + ib
then
arg(z) = arctan(b/a)
Let z' denote the conjugate of z. Therefore, z' = a - ib
Then
arg(z') = arctan(-b/a) = 2*pi - arctan(b/a) = 2*pi - arg(z)
Is every complex nberan imaginary number?
No. A complex number consists of a real part and a imaginary part. If the real part equals zero, there is only the imaginary left and you could therefor argue that it is an imaginary number (or else it would still be a complex number -with a real part=0)
Can you compare two complex numbers?
You can compare their magnitude (absolute values) but not the numbers themselves.
What complex number lies below the real axis and to the right of the imaginary axis?
Complex numbers whose polar representation is (r, theta) where 3*pi/2 < theta < 2*pi.
How do you graph x to the power of x with both the real and non-real parts?
This depends on what 'space' you want to plot it on. Another thing, are the x values all complex, or just real. I did a writeup on a similar question awhile back only considering real values of x, but complex values of y. For the positive sided, one way is to take the log of x^x, then you have log(y) = x*log(x). You can plot this manually on log paper.
If you use natural log, instead, then you have ln(y) = x*ln(x), then take e raised to both sides: y = e^(x*ln(x)).
To take natural log of a negative number, consider this:
if u = A*e^(iΘ), then ln(u) = ln(A) + (iΘ)*ln(e) = ln(A) + (iΘ)
Can you divide an imaginary number by a real number?
an imaginary number is imaginary so no (i guess) this answer kind of sucks
