When to use cos(omega*t) vs exp(j*omega*t)
When is it accurate to represent a signal voltage (in the example to follow, but the same question could be asked for current or electric field intensity or...) as V*cos(omega*t + phi) vs when the signal voltage must be represented as V*exp(j*[omega*t + phi])?
It's not an issue of accuracy, rather application. The cos(wt+phi) is a real function while the e^j*(wt+phi) is an analytic function, or phasor (typically used in RF texts with the wt (time varying term) dropped.
In general, I'd read up on analytic signals and get used to thinking in those terms, as they have practical uses in I/Q conversion, SDR (e.g. GNU Radio), and RF system simulation (e.g.) AWR VSS. It's really a method of representing signals by separating out the carrier and envelope (i.e. the baseband, modulation, information).
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