(b) 1z - 51 + |z + 1/ s |z - 21, find all z E C. Using z = a + ib: |z - 51 = 1x+iy -51 = 1(x - 5) + iyl = V(x - 5)+ |z + 11 = |x+iy+ 1/ = 1(x + 1) +iyl = V(x + 1) +y |z - 21 = 1x+iy - 21 = 1(x - 2) +iyl = V(x - 2) + y Hence, the statement can be rewritten as: V ( x - 5) ' + y + V (x+ 1) + y = V(x - 2)"+y [need to complete] End of assignment. MAR 12 8 -Explanation: To solve the inequality, we can square both sides: (V((x - 5)2 + y? ) + V ((x + 1)2 + 32) )2 s (v((2 - 2)2+ 12))2 Simplifying the left-hand side, we get: (x - 5)2 + yz + 2v((x- 5)2 + y?)v((x+ 1)2 + y?) + (x+ 1)2 + y? s(x- 2)2 + 12 Simplifying further, we get: (z - 5)' +2V((x - 5)' +y? )((x + 1)2 + y? ) + (x + 1)2 - (x-2)2 Expanding and simplifying, we get: x2 + 26x + y' + 26V((x - 5)2 + y?) ((x + 1)2 + y?)