Transfer function-leading and lagging

[pyroknife]

If we have the transfer function:
G(jw)=1/(1-j) where j=imaginary number

What is the output to input amplitude ratio and the phase relationship.

I'm confused about which one is the output and which is the input. I thought jw, the argument, is the input and everything on the right hand side is the output?

If so, this is not getting my the right answers that output to input amplitude ratio=1/sqrt(2) and that output leads input by 45 degrees.

 

[rude man]

If we have the transfer function:
G(jw)=1/(1-j) where j=imaginary number

What is the output to input amplitude ratio and the phase relationship.

I'm confused about which one is the output and which is the input. I thought jw, the argument, is the input and everything on the right hand side is the output?

If so, this is not getting my the right answers that output to input amplitude ratio=1/sqrt(2) and that output leads input by 45 degrees.

G(jw) = output/input.

The magnitude of G(jw) = |G(jw)| = sqrt(Re^2 + Im^2)
where Re = "real part" and I am = "imaginary part".

The phase of output/input is arc tan(Im/Re). Be careful to preserve the sign of the numerator and the denominator. Arc tan(-b/a) is not the same angle as arctan(b/-a).