Let {u1, u2} be an orthonormal basis for C2 and suppose that a vector z can be

Question:

Let {u1, u2} be an orthonormal basis for C2 and suppose that a vector z can be written as a linear combination
z = (5 - 7i)u1 + c2u2
(a) What are the values of uH1z and zHu1? If zHu2 = 1 + 5i, determine the value of c2.
(b) Use the results from part (a) to determine the value of ||z||2.