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Department of Computer Science and Engineering

1st Mid Exam

Course Title: Complex Variable and Matrices (MATH -2109)

Semester: 3rd | Session: 18-19

Time: 60 minutes | Marks: 20.00

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1)

Show that u(x,y) is harmonic. Find the harmonic conjugate function v(x,y) of u and the corresponding analytic function f(z) of Z, where u = y³ - 3x²y.

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5 Marks
2)

Prove that the complex function f(z) = sinx cos hy + i cos x sin hy is continuous as well as analytic at everywhere.

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5 Marks
3)

Find the inverse of the matrix

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5 Marks
4)

Find the rank of the matrix

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5 Marks
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Uploaded By: Onebyzero Edu July 28, 2024, 3:44 p.m.
Converted By (Img/PDF to Text): Baishakhi Bir Feb. 27, 2026, 9:04 p.m.
Reviewed By: Obaydul Hasan Nayeem March 1, 2026, 2:13 p.m.