Hi,
For the conjugate matching, just leave along the real part of your input impedance and conjugate the imaginary part.
-1+j is apparently the input impedance of a active component which is not practical when considering matching.
Conjugate mathcing can only ensure maximum power delivery but not the minimum reflection.
In short, for your case if you are going to conjugate match a A+jB impedance, just build a A-jB network.
Added after 2 minutes:
I don't konw if it is correct to say that you are designing a LNA or oscillator.
These are the fileds that we usually talk about conjugate matching when designing the input or output matching network.