Can we square root a negative number?
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Normally, when you square a real number, you always get a positive result. Like 2^2=4 or -2^2=4. This means that square root if 4 is either 2 or -2. But then what is the square root of -4???
Can we square root a negative number?
Squares are numbers multiplied by itself like 2×2 is 4 and -2×-2 is 4. So the rule is you can't ever get a negative number by squaring. As square roots undo squaring, there is no square root of a negative number.
But there is a popular quote that "Logic can take you from A to B, but imagination can take you everywhere." Keeping this quote in mind, mathematicians have found out a solution for this by the idea of an imaginary number system which totally opposite from the real numbers.
The Heron of Alexandria is regarded as the first one to conceive the idea of imaginary numbers. In that age, negative numbers were poorly understood by the people and this concept was even served fictitious by some people.
How to square root a negative number?
Imaginary numbers are basically not on the normal number line. They are written with an i. So now, the √-4=2i and basically, 2i×2i=-4. In mathematics, this concept is very useful for finding square root of negative number. For example, normally we cannot find √−25 but using imaginary numbers, √−25=5i.
They are used in many engineering disciplines because the letter i is used in many branches of engineering, particle physics etc.
Can a real number be operated with an imaginary number?
But remember, a real number cannot be operated with an imaginary number. They both are unlike quantities. Just like in physics, scalar and vector are unlike quantities.
As I said, a real number cannot be operated with an imaginary number, if the number is 0+1i, it is an imaginary number by the identity property of real numbers. And even 1+0i is a real number by the same property. But 1+1i is a complex number (For more information about complex numbers, click here).
So the short answer to the question, can we square root a negative number is yes...
Posts before October 2021 have been marked as "Old Posts". Less likely, but they might have out dated or incorrect information, ugly looking bits of code, no labels, etc. Don't get me wrong, many of these posts are top-notch and interesting too.
I thought it would be better not to delete or revamp these posts, even if they suck. The bitter truth is that old works always suck, but I take that as a positive tool to convey that I am growing. Besides there's no better way to showcase my journey without these old, messy, poorly written posts!
I thought it would be better not to delete or revamp these posts, even if they suck. The bitter truth is that old works always suck, but I take that as a positive tool to convey that I am growing. Besides there's no better way to showcase my journey without these old, messy, poorly written posts!
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