physics?

Girish Bhandari

Hello everyone,

If vectors(4x1) are in terms of Qr and Qi, where r is real and i is imaginary, functions of x and y, then they can also be represented in terms of Qr=qcos(theta) and Qi=qsin(theta), where 'q' is the magnitude and 'theta' is the phase.The magnitude 'q' and the phase 'theta' are also functions of x and y.

Now,If I take the derivatives of Qr and Qi with x and y, will those derivatives be the same as 'qcos(theta)' and 'qsin(theta)' w.r.t. x and y? Keep in mind that the magnitude and the phase is also function of x and y. One has to expand 'qcos(theta)' or 'qsin(theta)' by chain rule w.r.t. x and y.

Would these derivatives be able to represents the same physics?

-Girish