Question

What is conjugate of `i`?

Answer 1

The conjugate of `i` is `-i`

Explanation:

If `a, b in RR` then the conjugate of `a+ib` is `a-ib`.

When you have a polynomial equation with Real coefficients, any Complex non-Real roots that it has will occur in conjugate pairs.

For example, `x^2 + x + 1 = 0` has two roots: `-1/2+sqrt(3)/2i` and `-1/2-sqrt(3)/2i`.

`x^2+1=0` has two roots `i` and `-i`.

You could say that from the perspective of `RR`, the numbers `i` and `-i` are indistinguishable. When we extend `RR` to make `CC` we pick one of the square roots of `-1` and call it `i`. Then the other is `-i`, but they could just as easily be the other way around.