Complex Analysis - Maths KU

192 Chapter 4 Elementary Functions
In Problems 9–12, express the given function f in the form f(z) =u(x, y)+iv(x, y).
9. f(z) =e −iz
11. f(z) =e z2
10. f(z) =e 2¯z+i
12. f(z) =e 1/z
13. Use the sufficient conditions for differentiability from page 155 in Section 3.2
to determine where the function f(z) =e 2¯z+i is differentiable.
14. Use the sufficient conditions for differentiability from page 155 in Section 3.2
to determine where the function f(z) =e z2
is differentiable.
In Problems 15–20, find the image of the given set under the exponential mapping.
15. The line y = −2.
16. The line x =3.
17. The infinite strip 1