5. (17 points) Euler's identity and complex numbers. (a) (9 points) Use Euler's formula to prove the following identities: i. cos?(f) + sin?(f) =1 ii. cos(@+ 1) = cos(f) cos(v)) sin(0) sin(v)) (b) (8 points) Show that e/? = 2sin()e/l0+m/2 4 1. (c) (8 points) z(t) = (5 + v/25)e?*+2) and y(t) = 1/(2 ). i. Compute the real and imaginary parts of z(t) and y(t). ii. Compute the magnitude and phase of z(t) and y(t)