I am troubled with understanding freqency response. In lecture, my teacher talked about H(f), which i know means that the response depend on frequency, f. But when I read text book, it uses a differet notation H(jw), which i know that w is frequncy, but what is the character of j in that case? what does "jw" mean? and why is that ?

why V_L(jw) could be equal to V_L * e(j * phi_H)?

what is meant by e(j * phi_H)?

and how does the first row become the second row?

I know that is a bunch of question, thank you for your effort if you could help me with this.

besides, can anyone explain to my how lowpass filter works? some one tells me that because of frequency response, the unexpected low frequency will cause open loop in RC circuit, so the when the frequency is low, the circuit is open therefore filters out the low frequency, is that right?

I am troubled with understanding freqency response. In lecture, my teacher talked about $H(f)$, which i know means that the response depend on frequency, $f$. But when I read text book, it uses a different notation $H(j\omega)$, which i know that $\omega$ is frequency, but what is the character of $j$ in that case? what does "$j\omega$" mean? and why is that ?

why $V_L(j\omega)$ could be equal to $V_L e^{j \phi_H}$?

what is meant by $e^{j \phi_H}$?

and how does the first row become the second row?

I know that is a bunch of question, thank you for your effort if you could help me with this.

besides, can anyone explain to my how lowpass filter works? some one tells me that because of frequency response, the unexpected low frequency will cause open loop in RC circuit, so the when the frequency is low, the circuit is open therefore filters out the low frequency, is that right?