List of top Mathematics Questions on Complex numbers asked in AP PGECET

Let \( z \) be a complex variable and \( C : |z| = 3 \) be a circle in the complex plane. Then,

\[ \oint_C \frac{z^2}{(z - 1)^2(z + 2)} \, dz = \]

If the function \( f(z) = -x^2 + xy + y^2 + i(ax^2 + bxy + cy^2) \) of complex variable \(z = x + iy\) is analytic in the complex plane, then the values of \(a, b, c\) are _______

The value of the real variable \( x>0 \) that minimizes the function \( f(x) = x^x e^{-x} \) is ________

The complex-valued function \( f(z) = iz - |z|^2 \) is analytic at ...........