3 questions i need help on

Find a function f(z) such that the line below is the graph of the equation |z-3i|=|f(z)|. z is a complex number in the form a+bi in all 3 questions

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i know the equation of the line is y = x/2 + 1/2, but i don't know how to continue on

The square of the non-real complex number \(z\) is equal to \(\overline{z}\). What is the real part of z?

i wrote an equation that was \((a+bi)^2=a-bi\) and from there \(a^2 + 2abi - b^2 = a - bi\), but i don't know how to continue on from there

Find all complex numbers z such that\(|z - 3| = |z+i| = |z -3i|.\)

i tried writing some equations but it didn't work out