Harmonic Oscillator

Consider the 1-D harmonic oscillator, with Hamiltonian H=p²/2m+½mw²x²=hw(a†a+1/2), and with energy eigenstates H|n}=En|n}=hw(n+1/2)|n}. The eigenvectors of the annihilation operator a are known as coherent states: a|z}=z|z}, where z is in general a complex number (a is not Hermitian, so z is not necessarily real). Take |z} to be normalized: {z|z}=1.

a) Find and expression for |z} as a linear combination of the eneergy eigenstates |n}. Make sure it is normalized. Calculate {z1|z2}.

Please see attached for full question.
Also { and } are not the correct symbols, please see attached for proper format.