For the complex number question, just compare the mod arg form (which has an argument of 5pi/12), with the cartesian form. Equating imaginary parts will give u the answer. For the integrals, an odd/even argument for the first 2, and stating that since the function is always smaller than the other function when -1<x<1 means that its integral from -1 to 1 must also be smaller is enough.
