another complex question (1 Viewer)

[Gruma]

Q: define the modulus lzl of a complex number z. Given two numbers z1, z2 prove that the triangle represented by the complex numbers 0, 1, z1 is similar to the triangle represented by 0, z1, z1.z2????

 

[McLake]

If we take the corners 0,1,z1 and multiply those numbers by z2 we get 0, z2, z1*z2. The two triangles are similar.

Now i'm stuck ...

 

[spice girl]

Let A, B, C, D represent 1, z1, z2, z1z2 respectively.

In triangles OAB, OCD:

angle OAB = angle OCD (arg(z1z2) - arg(z2) = arg(z1) - arg(1))

OB/OA = |z1|/|1| = OD/OC = |z1z2|/|z2|

hence OAB similar to OCD (equal angle between two pairs of sides of equal ratio.