definitions of Re(z) and Im(z) Is it possible to derive a formula for Re(z) or Im(z) that does not use Re(z) or Im(z) in the formula? If so, what is it?
In other words, given any complex number z, where z = a+bi, and a and b are both real numbers, 
can we find a or b without using functions like Re(z), Im(z) or abs(z) (because abs(z) uses Re and Im in its definition)
Edit:I did not consider complex conjugation when writing this. I don't "accept" it because it is a function in terms of the individual real and imaginary components of z.

If you ''accept'' complex conjugation, then
$$\Re(z)=\frac{z+\overline{z}}{2}$$
and
$$\Im(z)=\frac{z-\overline{z}}{2i}$$
