Proof Complex Numbers: How to Prove |z1|^2/|z2|^2 = |z1/z2|^2

[Suni]

hello

could someone please help me out with proving the following:
|z1|^2/|z2|^2 = |z1/z2|^2

...with complex numbers

sorry I am not familiar with the coding here yet so i can't write that properly

 

[arildno]

How is division defined on the complex numbers?
Use that to get the result, alternatively use polar representation of the numbers.

 

[kendr_pind]

simply define z1 = a + jb and z2 = l + jm;
LHS - take modulus of each and keep it aside...i.e., a^2 + b^2 is modulus;
RHS - Rationalise the den. & num., i.e, z1/z2 = (a + jb)*(l - jm)/(l2 + m2);
seperate out the real & imaginary parts...u'll find LHS = RHS...