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Problem 2 Consider the set of functions {\fo), \fi), \f2}} defined on the perimeter of a circle of ra- dius R such that (0\fo) 02 + i, (0\fi) = i0 + 2, (0|f2) = 3i. Given the inner product (f|g) - sto f*(0)g(6)Rdo , use the Gram-Schmidt procedure on these functions, beginning with \fo) and pro- gressing to \f2), to create an orthonormal basis {loo), (01), (02)} for the set of polynomial functions of order 2 with complex coefficients on the specified interval. Express your final answer as functions of the real coordinate 0, namely (0|0i), and also provide (Pi) as linear combinations of \fi). Note: In Problem 2 you may use 3.14 for a and provide numerical coefficients to two significant figures in their real and imaginary parts. Problem 2 Consider the set of functions {\fo), \fi), \f2}} defined on the perimeter of a circle of ra- dius R such that (0\fo) 02 + i, (0\fi) = i0 + 2, (0|f2) = 3i. Given the inner product (f|g) - sto f*(0)g(6)Rdo , use the Gram-Schmidt procedure on these functions, beginning with \fo) and pro- gressing to \f2), to create an orthonormal basis {loo), (01), (02)} for the set of polynomial functions of order 2 with complex coefficients on the specified interval. Express your final answer as functions of the real coordinate 0, namely (0|0i), and also provide (Pi) as linear combinations of \fi). Note: In Problem 2 you may use 3.14 for a and provide numerical coefficients to two significant figures in their real and imaginary parts