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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.
You can work this out by using what we call "imaginary" numbers. By definition, imaginary numbers are numbers that when squared, will produce a negative value. Usually these are represented by multiplying real numbers by a constant called "i", which is defined as the square root of negative one.In this case the answer will be:x2 + 144 = 0∴ x2 = -144∴ x = -1441/2∴ x = 1441/2 * -11/2∴ x = 12i
The usual rules for "order of operation" apply. Don't forget that the square root of a negative number is an imaginary number. As an example, the square root of -9 is 3i (that is, the square root of +9, times the "imaginary unit").
An imaginary number is simply a number that contains 'i' which is simply shorthand for the square root of minus one. In the same way, we can write the square root of other negative numbers using i as a factor. For example;Sqrt(-64) = Sqrt(-1*64) = Sqrt(-1)*Sqrt(64) = i*8 = 8iThere are also 'complex numbers' which are simply combinations of real numbers (all positive and negative numbers) and imaginary numbers. For example;2+3iIs a complex number. Although these numbers seem not to "exist" (it's impossible to have a set of 8i golf balls, or for you to weigh 3i kg) they are very useful in the fields of mathematics, physics, and engineering, and allowing their existence can save a lot of trouble when it comes to doing difficult math.
using basic math principles, you can't find the square root of a negative number because in order for a number to be a square root, you have to multiply it by itself to get your radical. since a negative times a negative and a positive times a positive are both positive, it is impossible to find the square root of a negative number