In: Advanced Math
Prove the following formulas, where u, v, z are complex numbers and z = x +iy.
a. sin(u+v) = sin u cos v + cos u sin v.
b. cos(u+v) + cos u cos v - sin u sin v.
c. sin^2 z + cos^2 z = 1.
d. cos(iy) = cosh y, sin (iy) = i sinh y.
e. cos z = cos x cosh y - i sin x sinh y.
f. sin z = sin x cosh y + i cos x sinh y.