Complex no. geometry

Let mid - point of z1 and z3 be M, so M is 15/2 + 7i/2.
When M is translated to the origin, z1 is translated to (6 - 15/2) + (2 - 7/2)i
= -3/2 - 3i/2.
Similarly z3 is translated to (9 - 15/2) + (5 - 7/2)i = 3/2 + 3i/2.
Multiply these 2 new points by i will rotate them anticlockwise by 90 degree.
Which gives (-3/2 - 3i/2i)i and (3/2 + 3i/2)i , that is 3/2 - 3i/2 and - 3/2 + 3i/2.
Now translated them back to the position of M will give
z2 = (3/2 + 15/2) + (-3/2 + 7/2)i = 9 + 2i
z4 = (-3/2 + 15/2) + (3/2 + 7/2)i = 6 + 5i

2010-04-13 07:34:04 補充：
Answer : a = 9, b = 2, c = 6 and d = 5.

2010-04-13 07:47:08 補充：
The property of multiplying i will rotate a complex number anticlockwise by 90 degree is one of the reasons that makes complex number so important in studying engineering.