+2401 z = a + bi
|(a-3) + bi| = |a + (b+1)i|
sqrt(a^2 - 6a + 9 + b^2) = sqrt(a^2 + b^2 + 2b + 1)
a^2 - 6a + 9 + b^2 = a^2 + b^2 + 2b + 1
-6a + 9 = 2b + 1
8 = 6a + 2b + 1
7 = 6a + 2b
|z + i| = |z - 1 - 2i|
|a + (b+1)i| = |(a-1) + (b-2)i|
sqrt(a^2 + b^2 + 2b + 1) = sqrt(a^2 - 2a + 1 + b^2 - 4b + 4)
a^2 + b^2 + 2b + 1 = a^2 - 2a + 1 + b^2 - 4b + 4
2b + 1 = - 2a + 1 - 4b + 4
6b + 2a = 4
3b + a = 4
7 = 6a + 2b
3b + a = 4
a = 4 - 3b
7 = 6(4 - 3b) + 2b
7 = 24 - 18b + 2b
16b = 24 - 18b + 2b
16b = 17
b = 17/16
a = 13/16
There are probably other ones, but 13/16 + 17/16i is the one I found.
=^._.^=
