Problem 5
Problem 15
The harmanic conjugate of the function \(u(x, y)=2 x(1-y)\) is \(\ldots \ldots\)
Problem 21
Imnge of \(|z+1|=1\) under the mapping \(w=1 / z\) is......
Problem 33
The value of \(\oint\) cos z dr where \(C\) is the circle \(|z|=1\), is .....
Problem 44
The invariant points of the transformation \(w=(1+z)(1-z)\) are \(z\) :
Problem 49
If \(C\) in \(|z|=1 / 2, \int_{C} \frac{2^{2}-z+1}{z-1} d z=\)
Problem 50
Singular pointa of \(\frac{\text { con } \pi}{(z-1)(z-2)}\) are
Problem 57
The zeroes and singularities of \(\frac{z^{2}+1}{1-z^{2}}\) ure
Problem 58
Residue of \(\tan z\) at \(z=\pi / 2\) is \(\ldots \ldots\)
Problem 61
Taylor's series expansion of \(\sin z\) abeut \(z=\pi / 4\) is.
