Big thank youusing the identity
which will eventually simplify to which is
Big thank youCall them a,b,c instead for simplicity. A few things of note:
Also,
So,
To be honest, we don't need to use the fact that the conjugate is the reciprocal here, but it just made typesetting easier. The key is to use the fact that
then expand and equate
|z1+z2+z3| = |conj(z1+z2+z3)|Can some one show me the solution for the following question from Cambridge book
let z1,z2 and z3 be three complex numbers with modulus 1. prove that |z1z2+z1z3+z2z3| = |z1+z2+z3|