I have one qubit and I apply two gates to it: H and T, which yields the following superposition:
$$ \frac{1}{\sqrt{2}} |0\rangle + \frac{1+i}{2}|1\rangle $$
Now I want to calculate probability of 0 and 1 state:
$$ \left(A_1\right)^2 = \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{1}{2} $$ $$ \left(A_2\right)^2 = \left(\frac{i+1}{2}\right)^2 = \frac{i}{2} $$ $$ S = \left(A_1\right)^2 + \left(A_2\right)^2 = \frac{1+i}{2} $$ $$ P(A_i) = \frac{A_i^2}{S} $$ according to prior equations i receive following values $$ P(0) = \frac{1}{1+i} \land P(1) = \frac{i}{i+1} $$
I was expecting to get $A_i=0.5$ however $P(0) + P(1) = 1$
How do I interpret this results?