Give an example of a function ' W C ! C such that'.w C z/ D '.w/ C '.z/for all w; z 2 C
Chapter 3, Problem 9(choose chapter or problem)
Give an example of a function ' W C ! C such that'.w C z/ D '.w/ C '.z/for all w; z 2 C but ' is not linear. (Here C is thought of as a complexvector space.)[There also exists a function ' W R ! R such that ' satisfies the additivitycondition above but ' is not linear. However, showing the existenceof such a function involves considerably more advanced tools.]
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