(Sorry if this is a little big.)
I don't really know where to start. I substituted z = a + bi into the equation, but that didn't seem to help me.
2. Let g:[b, 2] --> R, where g(x) = 1 - x2, if b is the smallest real value such that g has an inverse function, find b and g-1(x).
I know that b = 0, but why? I can find the inverse function, but I can't quite grasp why 0 is the smallest value which allows g to have an inverse function.
I will offer half an appology to start with because you probably know a lot more than me
with the first one couldn't you just substitute in the value of z and then multiply top and bottom by the conjugate of the denominator
then put the real part=0 and the coefficient of i = 1 ?
I did it and I think it worked but I might have made a mistake.