Question

What is the conjugate of `i^2`?

Answer 1

Conjugate of `i^2` is `i^2` itself and not `-i^2`

Explanation:

Conjugate of a complex number `a+ib` is `a-ib`

as `i^2=-1+i0`,

its conjugate is `-1-i0` or `-1` i.e. `i^2` - in case you wish to write it this way.

Hence conjugate of `i^2` is `i^2` itself and not `-i^2`

Also if you mark a complex number `z` in Argand plane and its conjugate, the two are reflection of each other on real number line.

As `i^2=-1`, it lies on real number line and it will be its own reflection.