phase of a complex number signal

Question

How can I calculate the phase of $ \frac { e^{-i 2 \pi f T }} { 1 + i 2 \pi f T } $. This isn’t in the formula $ a + i b $ or $ A(f) e^{\phi (f) } $ where A is modulo and phi the phase of the complex number ? thank you

Answer 1

The phase is:$$\arg\left[ \frac { e^{-i 2 \pi f T }} { 1 + i 2 \pi f T }\right]=\arg(e^{-i2\pi f T} )-\arg(1+i2\pi f T) =-2\pi f T- \tan^{-1} 2\pi f T .$$