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Complex Analysis Quick Quiz

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Holomorphic concepts quiz

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Complex Analysis Quick Quiz
 

Complex Analysis Quick QuizOnline version

Holomorphic concepts quiz

by Yash GHODA
1

What term describes a function analytic on a domain in the complex plane?

2

Cauchy's integral formula requires the function to be analytic inside and on what geometric shape?

3

Which theorem states that a bounded entire function must be constant?

4

The maximum modulus principle says the maximum of |f| on a domain occurs where?

5

A Laurent series converges in which region around a point?

6

Which theorem relates a contour integral to the sum of residues inside the contour?

7

What type of singularity is a point where a function has infinitely many negative-power terms in its Laurent series?

8

If f is analytic and f'(z0) ≠ 0, what does f do to infinitesimal angles at z0?

9

What condition ensures a function is analytic on a region if CR equations hold with continuous partials?

10

Which type of singularity is a point where f has a finite principal part in the Laurent series?

Feedback

Holomorphic means complex differentiable at every point in the domain.

The formula holds for z inside the closed contour where f is analytic.

Liouville's theorem: entire and bounded implies constant.

For non-constant analytic functions, |f| attains its maximum on the boundary of a domain.

A Laurent series is valid in an annulus where the function is analytic.

Integral around a closed contour equals 2πi times the sum of residues.

An essential singularity has infinitely many negative-power terms.

Nonzero derivative implies f is locally conformal, preserving angles.

CR equations plus continuity imply analyticity in the region.

Poles correspond to finite-order principal part in the Laurent expansion.

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