1个
z2 + 3z + 1
dz
有两种不同的方式，即真正的积分
Z 2
0
1个
3 + 2吨
dt
被视为等于以下哪个值
4页
7
2个
3
2页
没有其他
请考虑以下语句：
（i）有一个全纯函数f：C！ C（Re（f（z））= x2
。
（ii）如果g：C！ C在C上是全纯的，然后f（z）= jzj
2个
g（z）是
在z = 0且g的每个零处均成立。
（iii）C上有一个全纯函数，使得f（
n + 1
n）= 0
对于n = 1; 2; ：：：并且f（0）= 1。
（iv）连续函数f：Cnf0g！如果Cnf0g C是全纯的
并且只有在
[R
对于Cnf0g中的每个闭合轮廓，f（z）dz = 0
下列哪一项是正确的：
（i）
（ii）
（iii）
（iv）
没有其
2.
Which one of the following statements about the complex dierentia-
bility of the function
f(z) = z + jzj
2
+ iz
is true
f(z) is holomorphic at 0 2 C
f(z) is dierentiable and holomorphic at i 2 C
f(z) is dierentiable at 0 2 C but is not holomorphic at 0 2 C
f(z) is dierentiable at i 2 C but is not holomorphic anywhere
in C
f(z) is not dierentiable anywhere in C
None of the others
3.
Let be the contour (t) = eit
; 0 t 2, parametrising the unit
circle. By evaluating the contour integral
Z
1
z2 + 3z + 1
dz
in two dierent ways, the real integral
Z 2
0
1
3 + 2 cos t
dt
is seen to be equal to which one of the following values
4 p7
p7
2
p3
2 p5
None of the others
Consider the following statements:
(i) There is a holomorphic function f : C ! C with Re(f(z)) = x2
.
(ii) If g : C ! C is holomorphic on C then f(z) = jzj
2
g(z) is dieren-
tiable at z = 0 and at each zero of g.
(iii) There exists a holomorphic function on C such that f(
n+1
n ) = 0
for n = 1; 2; : : : and f(0) = 1.
(iv) A continuous function f : Cnf0g ! C is holomorphic on Cnf0g if
and only if
R
f(z) dz = 0 for every closed contour in Cnf0g
Which one of the statements holds true:
(i)
(ii)
(iii)
(iv)
None of the others
