Ohhhh so you had to use the half-angle identity equation-- thank you so much haha!! I'll try and attempt the question again knowing the formula... thank you so much once again!! Also I understood the concepts on the 2nd and 3rd question on where I went wrong and how to do the question it self. this is really helpful!!

I'm so dearly sorry !! I just read the guidelines saying one question per post.. I won't repeat the same mistake next time-- though could I seek help on these just this once?? I'm so confused

ya sure my algebra went like this:

|f(z)-z|=|f(z)-0|

|wz-z|=|wz|

factor

|w-1||z|=|w||z|

|w-1|=|w|

(a-1)^2+b^2=a^2+b^2

-2a+1=0

a=1/2

and then i think i plugged it in

are those steps above right?

bcs if so I messed up on the plugging it in part