Math Problem Solver

2-11

CAUCHY-RIEMANN EQUATIONS

Are the following functions analytic? Use (1) or (7).

2. f(z) =iz overline z

3. f(z) = e ^ (-2x) * (cos 2y - i * sin 2y)

4. f(z) = e ^ x * (cos y - i * sin y)

5. f(z) = Re(z ^ 2) - iIm(z ^ 2)

6. f(z) = 1 / (z - z ^ 5)

7. f(z) = i / (z ^ 8)

8. f(z) = Arg * 2pi*z

9. f(z) = 3pi ^ 2 / (z ^ 3 + 4pi ^ 2 * z)

10. f(z) = ln|z| + iArgz

11. f(z) = cos x * cosh(y) - i * sin x * sinh(y)