• # What is the meaning of imaginary value in maths?

Want to know the meaning of imaginary value in mathematics? Searching for its real world equivalent online? Here, scroll through this Ask Expert page and get answers to your questions.

We often hear this term: imaginary value or imaginary number used in maths and other interconnected areas such as physics and computer science. What are it's real world equivalents. Does it refer to a certain object a certain kind of mathmatical or logical object or is it simply a calculating tool to ascertain a given value like in complex numbers which are assumed to be part real and part imaginary. Exactly how does this map in real world scenario. Can experts please explain this in a more elaborate manner?

• Imaginary values implies wasted or not useful values. While carrying out some work, there will be useful work and some of the work will not be counted for (some imaginary work will be required to carry out the useful work). Those unaccounted values are expressed in terms of imaginary values.

• An imaginary value or number is not a real value. It us denoted by i. It is a symbol of square root -1. Or i square =-1.

A real number gives always a positive real number when multiplied by itself or squared. For example.
1 x 1 = 1 (positive real number)
-1 x -1 = 1 (positive real number)

But an imaginary number (i) can give a result:
ix i= -1
If we take the square root of both sides, then we can get the result:
i square = square root -1
Square root of -9 will be 3i.

Hence, this imaginary value is very useful to solve the things need the square root of a negative number.

• In Mathematics, there are certain problems which cannot be solved using the concept of real numbers and to overcome that the imaginary numbers were conceptualised. Later they became useful in understanding certain problems in terms of complex numbers and solving them using the real part and imaginary part. So, there is a use of these imaginary numbers in frequency spectrum analysis, Fourier analysis, Quantum mechanics etc where complex numbers are used to find out certain solutions which cannot be arrived upon using simply the real numbers.

Let us try to understand it from a simple equation which we want to solve -
X^2 + 1 = 0

If I want to solve it then I get X = under root of (-1)
We do not have a real number as under root of a negative number and hence we are stuck at this point and that is where in Mathematics an imaginary number known as 'i' was introduced to denote the under root of minus one. This made life simpler and wherever we were stuck with this we represented it with i and soon it became a well established part of the Mathematical calculations especially in solving the complex scientific problems.

One interesting which was found with logic was that if there are two complex numbers which were equal to each other then we could make their real and imaginary parts also equal to each other and that helped in deriving many things in complex wave analysis like done in the fourier transform.

So in our day to day life we do not perceive any use of these imaginary numbers but they have their utility in advanced computations in Scientific formulations.

Knowledge is power.

• An imaginary number is a number that gives a negative result when squared.
We all know that any number square will be positive only, for example, 7 X 7= 49 or -7 X -7 = 49. We all know that two negatives when multiplied will become positive. Any real number when you multiply with the same number you will get a positive number or Zero.
Let us imagine that there is a number for which a square is a negative number. The square root of -1 is the unit number here. This square root of -1 is taken as i.

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• Imaginary number is the product of a real number with which an imaginary unit is multiplied. As for example the imaginary part will appear as iy where i is the imaginary unit where as y is the real number.
maginary quantity i is referred to the square root of -1.
It has wide application in solving the problems related to Electrical Engineering where i is often replaced by the letter j so as not to create any confusion with the symbol of the current usually represented by the letter i.
The charecterstics of the imaginary quantity is such that square of these units will follow the sequence of numbers like -1, -3, -5, -7 and so on. In nut shell, we can say that any the squares of such product will show the negative part of any odd numbers.

• Basically, the concept originates back to the solution of quadratic equation: x^2+1=0.
This means squared a number results in negative outcome which is not possible for any real values. To find the answer of this question Complex Numbers were introduced:
C= x+iy, where x and y both are real numbers. and i is under-square root -1. which makes x as the real part of C and y as the imaginary part of C.
Later, it was found that the assumption of i is useful for many other applications in Physics and Advanced Mathematics which are described in the above answers.
The geometric representation of abstract variables have beenon of the major significance of complex mathematics such as in phasor diagram representing electric current and potential in different axes, topological programming etc. Hope, you got your answer.

• In mathematics, imaginary value is used for solving many problem. The term "imaginary" is used because of absence of real number having a negative square. The letter i is used to signify that a number is an imaginary number. It stand for the square root imaginary numbers. When you square imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is denoted by its property i2 = -1. The square of an imaginary number bi is -b2. You can understand this way-
5i is an imaginary number, and its square is -25.
The letter i is a number, which when multiplied by itself gives -1. This means that
i = v - 1.
It is widely used in the field of electrical engineering.