An Argand Diagram is a graphical representation of a complex number. The real part is the horizontal coordinate, and the imaginary part is the vertical coordinate. See Related Link at Wolfram MathWorld.
The basic theory of imaginary numbers is that because (-) numbers squared are the same as (+) numbers squared there is not a correct continueos line on a graph.
Caspar Wessel, a Norwegian and Danish mathematician was the first to porpose representing complex numbers in a two dimensional plane using real and imaginary axes. The idea was developed by Jean-Robert Argand, a Frenchman.
In the Argand diagram (complex plane), numbers on the horizontal axis represent real numbers.
Yes, over the real set of numbers. For example, the graph of y=x2+1 is a regular parabola with a vertex that is one unit above the origin. Because the vertex is the lowest point on the graph, and 1>0, there is no way for it to touch the x-axis.NOTE: But if we're considering imaginary numbers, the values "i" and "-i" would be the zeroes. I'm pretty sure that all polynomial functions have a number of zeroes equal to their degree if we include imaginary numbers.
No. Irrational numbers are real numbers, therefore it is not imaginary.
A complex number, z, may be written as z = x + iy where x and y are real and i is the imaginary square root of -1. x is the real part of z and iy is its imaginary part. The Argand diagram for z would show it as if it had the coordinates (x, y) in the Cartesian plane. However, where the Cartesian plane has the x-axis the Argand diagram has the real part, and where the Cartesian plane has the y-axis the Argand diagram has the imaginary part. Equivalently, z can be defined in terms of polar coordinates: z = (r, q). This is the same as z = rcosq + i*rsinq, so the real part is rcosq.
No difference. The set of complex numbers includes the set of imaginary numbers.
'Complex numbers' are numbers that comprise 'real' and 'imaginary' numbers. In electrical engineering, we identify 'imaginary' numbers by placing a lower-case 'j' in front of them. For example, the complex number (10 + j5) comprises the 'real' number, 10, and an 'imaginary' number, 5. We use complex numbers to locate points on a graph. Mathematicians call the horizontal axis of a graph the 'real axis', and they call the vertical axis the 'imaginary axis'. So 'imaginary' doesn't mean something that only exists in the mind, it's simply a mathematical term for the vertical axis of a graph. So the complex number (10 + j5) is used to represent a point which is located 10 units along the positive horizontal axis and 5 units along the positive vertical axis. In alternating current theory, we use 'phasors' (a type of vector) to represent voltages or currents that lie at different angles to each other, so we can define them in terms of horizontal and vertical axes. In other words, every phasor can be defined in terms of real and imaginary numbers. We can then use the rules of 'complex mathematics' to multiply, divide, add, or subtract phasors -but that's another story!
No, it is imaginary. Irrational numbers are a subset of real numbers Real numbers and imaginary numbers are sets without any overlap.
Émile Argand died in 1940.
Émile Argand was born in 1879.
Yes, imaginary numbers are a subset of complex numbers.
The graph of imaginary numbers takes two axes. A part for the real part and the i part.
Imaginary numbers are not a subset of the real numbers; imaginary means not real.
2 does belong to the set of imaginary numbers. Any real number is also imaginary. Imaginary numbers are the set of all numbers that can be expressed as a +b*i where "i" is the square root of negative one and "a" and "b" are both real numbers.
Aimé Argand was born on 1750-07-05.
Aimé Argand died on 1803-10-14.
imaginary numbers are numbers that are a negative square root, which is not possoble therefor it is called and imaginary number. ex the square root of -24 is an imaginary number
In mathematics, an imaginary number is a number whose square is a negative real number and written in the form bi where i is the imaginary number √(-1) and b is real.A complex number is a number with both real and imaginary numbers, such as (3+2i), where 3 is real and 2i is imaginary.Imaginary numbers were 'invented' by Gerolamo Cardano in the 1500's while solving cubic and quartic equations although it is said he did not understand their properties, and they were not properly defined until 1572 by Rafael Bombelli, although he did not name them imaginary numbers.The name came from Descartes in his book "La Geometrie" where it was meant to be derogatory and sarcastic, as the number √(-1) was thought not to exist by many mathematicians. It was not until the work of Euler in analysis that the imaginary number i was properly understood and widely acknowledged as being a proper numberAnother AnswerMathematicians call the horizontal and vertical axes of a graph, the 'real' and 'imaginary' axes. Numbers lying along the real (horizontal) axis are called 'real numbers', and numbers lying along the imaginary (vertical) axis are called 'imaginary numbers'.(see first discussion page entry)
The answer will depend on what numbers you wish to graph.
Jean-Robert Argand was born on 1768-07-18.
Jean-Robert Argand died on 1822-08-13.
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
Imaginary numbers are only ever used when you are using the square roots of negative numbers. The square root of -1 is i. You may find imaginary numbers when you are finding roots of equations.