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If we wanted to get a vector with the angle theta1 - theta2, would we take the inverse of z2 and multiply it with z1?


For complex numbers z_1 and z_2 expressed in polar form, their complex division would give z_1 / z_2 = (r_1 / r_2, \theta_1 - \theta_2). So yes, that would be a way to produce a complex number with angle \theta_1 - \theta_2.