Expand ψ(o) in terms of eignestates

[M. next]

if ψ(o)=(1 0)$^{T}$ at time t=0.

According to some Hamiltonian, it was found that the corresponding eigenstates are |ø$_{1}$> = 1/√2(1 i)$^{T}$ and |ø$_{2}$> = 1/√2(1 -i)[itex]^{T}

so then we wanted to expand ψ(0) in terms of |ø$_{1}$> and |ø$_{2}$>:

the author got: 1/√2|ø$_{1}$> + 1/√2 |ø$_{2}$>

My question is that where did he get the coefficients of |ø$_{1}$> and |ø$_{2}$>?? Is there a certain rule to this?

Note: this is an easy example, I can give a more detailed one if needed.

 

[ChrisVer]

Just solved this:
$\psi(0)= a |1> + b |2>$
for $a,b$