GRE Subject 2026 Practice Test Maths Complex Analysis Free Quiz 2

11. What singularity is neither removable nor a pole?

A. Removable B. Pole C. Branch D. Essential

12. What is the Cauchy integral formula?

A. f(z0) = (1/(2πi)) ∮ f(z)/(z - z0) dz B. f(z0) = (1/(2π)) ∮ f(z)/(z - z0) dz C. f(z0) = (1/(2πi)) ∮ f(z) dz D. f(z0) = (1/(2πi)) ∮ f(z)/(z - z0)^2 dz

13. What does the residue theorem state?

A. Zero B. Infinite C. 2πi ∑ Residues D. Negative

14. What is a branch cut?

A. Contour B. Singularity C. Pole D. Branch cut

15. What principle relates the change in argument to zeros and poles?

A. Argument principle B. Residue theorem C. Cauchy integral D. Liouville's theorem

16. What type of mapping preserves angles?

A. Linear B. Affine C. Conformal D. Projective

17. What is the form of a Möbius transformation?

A. f(z) = az + b B. f(z) = z^2 C. f(z) = e^z D. f(z) = (az + b)/(cz + d)

18. What is a fundamental domain for functions like z^n?

A. Unit circle B. Real line C. Upper half-plane D. Imaginary axis

19. What does Liouville's theorem state about a bounded entire function?

A. Analytic B. Continuous C. Differentiable D. Constant

20. What series generalizes the Taylor series for functions with singularities?

A. Taylor B. Laurent C. Maclaurin D. Fourier

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