# Understanding Complex number

1. Apr 14, 2017

### 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???

2. Apr 14, 2017

### Staff: Mentor

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

3. Apr 14, 2017

### Gourav kumar Lakhera

Thnkuu buddy

4. Apr 14, 2017