1. The problem statement, all variables and given/known data So I've got two problems I'm struggling a bit with. One of them I've solved (I think), but I'm definitely not sure. The other one is bugging me a bit. Anyway: i] Determine all z∈C so that |z - 1| = 5 and |z - 4| = 4 ii] Determine all z∈C so that |4 - z2| = z 2. Relevant equations 3. The attempt at a solution i] I say that z = x+yi as a starting point. From there: |x + yi -1| = 5 √( (x - 1)2 + y2 ) = 5 x2 + 1 -2x +y2 = 25 |x + yi -4| = 4 √( (x-4)2 + y2 ) = 4 x2 + 16 - 8x + y2 = 16 y2 = 8x - x2 Inserting this in the first equation: x2 + 1 - 2x + 8x - x2 = 25 6x + 1 = 25 x = 4 and then y2 = 32 - 16 = 16, y = ± 4 So I get z = 4±4i I think this should be correct, but I'm a bit.. unsure. ii] I've gotten so far that I've looked at the exercise and realised that the absolute value of someting is always a real number, which means if z = x+yi, then y=0. But from here I'm unsure on how to proceed. How on earth am I supposed to solve this? I'm feeling.. lost.