Now realized that Mitchell said he has MMA 9. To/FromPolarCoordinates are new in 10. So:
toPolarCoordinates[vect : {x_, y_}] := {Norm@vect, ArcTan[x, y]} fromPolarCoordinates[{r_, ?_}] := r {Cos@?, Sin@?}
This is one way of many:
phasorAdd°[{rA_, ?A_}, {rB_, ?B_}] := MapAt[ #/°&, ToPolarCoordinates[ FromPolarCoordinates[{rA, ?A °}] + FromPolarCoordinates[{rB, ?B °}] ], 2 ] phasorAdd°[{5, 36.87}, {10, -53.13}] {11.1803, -26.5649}
In[1]:= eq1 = a1 Exp[I ( \[Omega] t + \[Phi]1)] + a2 Exp[ I (\[Omega] t + \[Phi]2)] Out[1]= a1 E^(I (\[Phi]1 + t \[Omega])) + a2 E^(I (\[Phi]2 + t \[Omega])) In[2]:= eq2 = CoefficientList[eq1, Exp[I \[Omega] t]] Out[2]= {0, a1 E^(I \[Phi]1) + a2 E^(I \[Phi]2)} In[3]:= eq3 = eq2[[2]] /. { a1 -> 5, a2 -> 10, \[Phi]1 -> 36.87 Degree, \[Phi]2 -> - 53.13 Degree} Out[3]= 10. - 4.99998 I In[4]:= {1., 1./Degree} * CoordinateTransform["Cartesian" -> "Polar", ReIm[eq3]] Out[4]= {11.1803, -26.5649}
You can replace the Cos[x] by a complex exponential E^(I x). All operations are easier with the exponentials. At the end, take the real part of the result.