20121218311

1) f{z)— z", n = 1,2,...

/(z) = rV'^,<p = r" (cos(/7<$!) + i sin(/7#?)) n(ł\<p)= r" cos(n(p\ v(r,(p)-rⁿ smynę).

2)    f(z)-e^z - e^xe^iy = e^T(cos(v)+/ sin(v u(x, y) = e^x cos(y), v(.v, v) = e^T sin(7)

3)    /(z)=sm(z)=J_r[e^&-«*]= j-[e“e~^f -e'V]

= [cos(jt](e~' -e')+ isin(x)(e~' + e’ )]

= sin („r)cosh(y)+i cos(jc)sinh(y)

4)    /(z) = yfz = z^lln = r^{h n}e^lcpni - jest n - znaczna np. n = 3

/₀ (z) = V^^/3, J (z) =    , /, (z) = V^^(?,+4'^t)/;