Complex number representations (1 Viewer)

[HSC2014]

On the argand diagram A, P, Q respectively represent complex numbers 1, z1, z2. Construct point R such that the triangles OAP and ORQ are similar. Hence, find the geometrical meaning of the point R.
I have no clue; could someone help please? Thanks

 

[billym]

Draw a diagram, and place R where you think it should go.

Using the similarity of the two triangles, try to find a relationship between the modulus of R (say z3) and the moduli of z1 and z2. Then try to do the same with the arguments. You should find a nice little result for z3 in terms of z1 and z2.

 

[HSC2014]

Hmm... from "OAP ||| ORQ" I can get:
OR/OA = OQ/OP (corresponding sides)
OR = OQ/OP
i.e. |z3| = |z2|/|z1|
Hence arg (z3) = arg z2 - arg z1?

Therefore z3 = z2/z1 ?

I feel dodgy LOL

 

[hit patel]

hmm....
Basically its telling you to find the coordinate on the complex plane R as I think while doing it geometrically. This is how I did these kind of questions.
Therefore please view image:



Well PLease tell me if this is right and Others please correct me If it is wrong.
Also Please keep posting up questions

Cheers

 

[HSC2014]

Not quite the reverse since you use point R = z1z2. In the question I posted above, I am trying to prove that point R = z1z2 (if that is correct).

 

[hit patel]

Therefore is my answer wrong?

 

[Drongoski]

See Fig 2.35, P53 of Cambridge 4U text.

 

[hit patel]

Oh ok. Right that is what you mean HSC2014. Hahaha I took the wrong corresponding sides cos no diagram. So sorry . . Yeah that is how u do it hs2014. See if you get anywhere from continuing my way... :_( ....