Can you, please help me with this:

(a) Show that if C is in Mn(C) is Hermitian and x*Cx = 0 for all x is in Cn, then C = 0.

(b) Show that for any A is in Mn(C) there are ( unique ) Hermitian matrices B and C for which A = B + iC.

(c) Show that if x*Ax is real for all x is in Cn, then A is Hermitian.

Thank you!