I'm doing some AC circuits problems and it involves complex numbers.
In the textbook, it was given that the multiplication of complex numbers, in polar form is:
$$z_1 \cdot z_2 = r_1 r_2 \angle (\phi_1 + \phi_2)$$
and using $R \angle (\phi) = R e^{i(\phi)}$.
Multiplying $$(5.01 e^{i(-11.3)}) \cdot(100 e^{i60}),$$ I get $$501e^{i48.7}$$ as an answer. ($501 \angle(48.7)$)
However, using Wolfram Alpha, the answer shows as $501e^{i(-89.69)}$. ($501\angle(-89.69)$).
Please help me clear things up. Thank you.
edit: angles are in degrees.
Wolfram Alpha gives a slightly different answer than you wrote here: namely, it gives the angle in degrees ($\theta = -89.6955°$) whereas you give your angle in radians ($48.7$).
$e^{i\theta}$ is periodic, with period $2\pi$. If you subtract $16\pi$ from your angle you get $-1.565482$ radians: converting that to degrees by multiplying by $\frac {180°}{\pi}$ you get Wolfram's $-89.6955°$.
So your answers agree, you just use different units, and Wolfram used the reduced reference angle.