How Do You Solve a Complex Number Problem Involving a Parallelogram?

[PuzzledMe]

(Self-solved) Need help with complex number question

Homework Statement

I'm looking at this question while practising and I still don't really understand the question entirely. I'm extremely bad with this chapter, not very good at understanding questions and am in need of some help or guidelines with going about doing it.

"The parallegram OABC, described in an anticlockwise sense where O is the origin, lies in the first quadrant in which OA = 3 OC and ∠COA = 30 °. The vertices A, B, C represent the complex numbers a, b, c respectively. Express the complex number c/a in polar form.

Given that a = 6 + i, find b and c in their simplest exact form."

I'm really not sure if parellegram refers to parellelogram but either way, I'm still stuck.

I'm given these solutions for this question.

1/3 (cos 30 ° + i sin 30 °); b = (35/6 + √3) + (2 + √3/6 i), c = (√3 - 1/6) + (1 + √3/6 i)

Homework Equations

1st try (no success): I tried using cosine/sin rules here though.
2nd try (some success): I used multiplication/addition rule for complex numbers...

The Attempt at a Solution

For the first part, I was thinking that since OA = 3OC, OC is 1/3 of OA and hence the answer but my gut feeling was that my logic was way too simple..

For second part, I tried using the following. This is the way I see the question:

http://i258.photobucket.com/albums/...help/complexnumbers/pic1_ltbook_complexno.png

http://i258.photobucket.com/albums/...help/complexnumbers/pic2_ltbook_complexno.png

http://i258.photobucket.com/albums/...help/complexnumbers/pic3_ltbook_complexno.png

What I got was c = 1/6 √111 + (1/6 √37) i
I don't know where I've gone terribly wrong, and felt discouraged so I did not do calculations for b...

 

[PuzzledMe]

I think I thought too far for this one, managed to get c now without drawing any pictures...I'll try B later but I have no idea what to do from now also...

 

[PuzzledMe]

Ok stupid me managed to solve it...a + c = b...
I feel like a noob...