Question

What is i times -i?

I looked it up and it's 1, but how?

Answer 1

\(i*-i=-i*i=-\sqrt{-1}\sqrt{-1}=-(-1)=1\)

Answer 2

\(\sqrt{a}\sqrt{a}=a\)

Answer 3

by definition we have:
\[i ^{2}=-1\]
and please note that:
\[i*(-i)=-i ^{2}\]
so?