Discovering vertices of a rectangle in an Argand diagram

Hi Mr Koh,

                  How do I do this question- In an Argand diagram, the points A, B, C and D represent the complex numbers a,  -2+5i,  c   and  3/2 - 1/2 i   respectively. Given that ABCD is a rectangle described in the clockwise sense with BC=2AB, find a and c.

                  I tried drawing B and D on the same diagram but they don't even have a right angle between them, so how can it form a rectangle? And I can't place points A and C on the diagram because they said ABCD is read clockwise but it is also mentioned BC=2AB....so I am lost. Haha. Thanks Mr Koh!

Student X

                     Based on the construct described, the rectangle's length is twice its breadth. I would recommend drawing a generic upright rectangle instead of trying to place the points specifically in Argand space. Do note that vectors are involved in the solving process. I have drafted a solution template for you:

Hope this helps. Peace.

Best Regards,

Mr Koh