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I repeated it because of this:
I wanted him to be sure that the answer is only 3. 1 answer not 2.
But, what you said in #93 was already told and did not need repeating.
Nope, I was dealing with a far more important concept and did not answer that question. Do you see it now?
Actually, #94 is me feeling you have not understood the question.
Everything you are saying is true but you are missing the point of my post #93 which essentially makes your post #94 non - essential.
We could, but, there is still no special name for non-principal roots.
We could say it is the root of the equation x^2 - 9 = 0.
He is asking this:"If we call 3 the principal square root of 9, then what kind of square root of 9 is -3?". The answer is that there is no name given to it.
When 9 is in the square root sign that means principal square root, just the 3.
Thanks for that!
It was called imaginary because in the beginning when the concept of the root of a negative number was proposed most mathematicians did not like it. They called them imaginary numbers to sort of poke fun at the whole idea. Later, as it caught on, complex numbers was name given for them.
Please do you have an idea as to why it is called complex or imaginary?
Both 3 and -3 when squared are 9. But only 3 is the principal square root.