课程名称︰工程数学-复变
课程性质︰电机系大二必修
课程教师︰林坤佑
开课学院：电机资讯学院
开课系所︰电机工程学系
考试日期（年月日）︰2018/03/20
考试时限（分钟）：50分钟
试题 :
1. If z = -√3 + i, please express ln(z) in the form of a + ib.(25%)
2. Show that the f(z) = z-bar^2 is not analytic at any point.(25%)
3. Prove that |cosh z|^2 = cos^2(y) + sinh^2(x).(25%)
4.
(a) Verify the function u(x, y) = e^x(xcosy - ysiny) is harmonic.(10%)
(b) Find v(x, y) which is the conjugate harmonic of u(x, y).(15%)