Question

Answer to this equation |z+3|=|z-2|

Answer 1

The equation |z + 3| = |z - 2| can be solved by first considering two cases:

z + 3 = z - 2

Adding 3 to both sides and subtracting z from both sides gives:

6 = -2

This is a contradiction, so this case has no solution.

z + 3 = - (z - 2)

Adding 3 to both sides and subtracting z from both sides gives:

1 = -2z

z = -1/2

So the only solution to the equation |z + 3| = |z - 2| is z = -1/2.