Why doesn't √-1×√-1 always equal 1 in complex numbers?

[Gourav kumar Lakhera]

As we know that √-5×√-5=5 i.e multiplication with it self
My question is that according to this √-1×√-1=1.but it does not hold good in case of i(complex number).
I.e i^2 =-1. Why?

 

[Mark44]

As we know that √-5×√-5=5

No, this is not true. $\sqrt{-5} = i\sqrt{5}$ so $\sqrt{-5} \cdot \sqrt{-5} = i^2 (\sqrt{5})^2 = -5$, not 5 as you show above.

i.e multiplication with it self
My question is that according to this √-1×√-1=1

This isn't true, either, for the same reason as above.

.but it does not hold good in case of i(complex number).
I.e i^2 =-1. Why?

You are apparently using the rule that $\sqrt a \sqrt b = \sqrt{ab}$. That rule holds only when both a and b are nonnegative real numbers.

 

[Gourav kumar Lakhera]

Thnkuu buddy

 

[fresh_42]

You might want to read this insight:
https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/