課程名稱︰工程數學-複變
課程性質︰必修
課程教師︰陳士元
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰104/4/7
考試時限（分鐘）：110分鐘
試題 :
COMPLEX ANALYSIS
Quiz 1 (陳士元老師班)
_2
1. Find the image of the line Im(z) = 1 under the mapping f(z) = z .(10%)
-1 -1
2. Find the derivative of tanh (z) + cosh (z) ar z = -√2 .(10%)
2 2 2 2
3. If f(z) = (ax + xy + by ) + i(cx + xy + dy ) is an analytic function in
domain D, find a, b, c, and d.(10%)
4. Find all values of the given quantity. (10% each)
i
(a) (1 + i)
i
(b) ln(i )
-1
(c) cos (i)
5. Evaluate the given integrals along the indicated contour C. (10% each)
1 3
(a) ∮ ────────── dz , C: |z| =