Let be the set of all real-valued integrable functions defined on the interval[a, b]

Chapter 6, Problem 4

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Let be the set of all real-valued integrable functions defined on the interval[a, b]. Then (, +) is an algebraic structure, where + is the addition of h(a + bi) = (a, b)(, ) ( , )( , ) (a, b) (c, d) = (ac bd, ad + bc).(, )(, )(, +)(, +) (x) = x2.(+, )(+, )(+, +)(+, +)(x) = x. ++(4, +).) (4, +).li lilililili (G, ) (, )li l1 = [i i 11]. = [1 1 i i],l1 li = [1 1 i i], = [i i 1 1].304 CHAPTER 6 Concepts of Algebrafunctions. Define by Use yourknowledge of calculus to verify that I is an OP map.