for all X not equal to Y should sqrt X also not equal to sqrt Y? even for complex nos?

Question

FOR ,X NOT=Y
sqrtX NOT=sqrtY is true for all x&y?

I WANT TO KNOW IF IT IS ALSO TRUE FOR COMPLEX NOS

Answer 1

Yes, that's true. For suppose that √x = √y. Then (√x)² = (√y)². But by definition of √, (√x)² = x and (√y)² = y, thus x = y. Taking the contrapositive, x≠y ⇒ √x≠√y. This holds regardless of which branch of the square root function is chosen.

Answer 2

Yes,
Consider Positive = it is not equal
Consider Negative = It is not equal neither.

Regards


Zain

Answer 3

Ok, your question is oddly worded, please re-word it's hard to tell what you are asking.