Real Variables In Complex Equation

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Dr_Seuss
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Hi

Homework Statement


The problem asks to put the following expressions in z={ReA(e^i*)(e^i*)} Form

for

z=3cos(wt)-sin(wt)

z=sin(wt+pi/4)+cos(wt)

z=sin(wt)+2cos(wt-pi/3)-cos(wt)


Homework Equations





The Attempt at a Solution



The problem is I don't even know which parts are real and imaginary because there is no i value in any of them. I used eulers equation and expand them but arrived at a equation with only one i, two cos, and a sin. Is this the right approach or am I missing the point.

Thanks
 
Does this make any sense?
 
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  • Handwritten derivation using Euler's formula: Ae^(iθ) = A[cosθ + i sinθ], Re Ae^(iθ) = A cosθ, Ae^(i[π/2 - θ]) = A[sinθ + i cosθ], Re Ae^(i[π/2 - θ]) = A sinθ, Z = 3cosωt - sinωt = Re[3e^(iωt) - e^(i[π/2 - ωt])], and Ae^(iθ)e^(iα) = Ae^(i(θ+α)) with real parts A cos(θ+α) and A sin(θ+α).
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Ya That does help a lot does this mean for

z=sin(wt)+2cos(wt+pi/4)-cos(wt)

The Real Part would be

Re{e^i(wt-pi/2) + 2e^i(wt-pi/3) - e^i(wt)}

in complex phasor amplitude

Thanks