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If you have a complex function in the form "a+ib", the (complex) conjugate is "a-ib". "Conjugate" is usually a function that the original function must be multiplied by to achieve a real number.
If the first derivative if a function is a constant that the original function has only one slope across its entire domain, so it is a line.
Multiplying a function by -1 will make it a reflection of the original function across the x axis.