Define a function f(x + iy) = (e^x)(cos y + isin y).

a) Show that f is injective (one-to-one) on the strip S := {x + iy : −π < y < π}.

b) What is f(S)?

c) Find the (unique) inverse of f mapping f(S) back to S.

Answer rating: 100% (QA)

To show that the function fx iy excos y isin y is injective on the strip S x iy y we need to demonstrate that different complex numbers in S map to di... View the full answer