# Understanding Complex number

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
Mentor
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.
Gourav kumar Lakhera said:
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.
Gourav kumar Lakhera said:
.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.

Thnkuu buddy