List questions from rouches-theorem

Published on 14 Apr 2026 - 2:47

74

Views

Finding number of roots to an equation

Published on 11 Apr 2026 - 0:27

427

Views

Showing that, for $|a|>3$ and $n\geq1$, the function $f(z)=e^z-az^n$ has exactly $n$ roots (all simple and different) in the open unit disc

Published on 13 Apr 2026 - 21:05

401

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Using Rouché's theorem to bound zeroes of partial sums of $e^z$

Published on 13 Apr 2026 - 22:28

357

Views

Prove that $ze^{\lambda - z} - 1$ has a real root in the unit disk

Published on 15 Apr 2026 - 16:37

438

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Roots of $z \sin(z) =1$

Published on 15 Apr 2026 - 18:24

98

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Solving non-homogeneous system of equations with Rouche Capelli theorem

Published on 13 Apr 2026 - 8:50

80

Views

Confusion in the proof of Rouché's theorem (joint continuity part)

Published on 10 Apr 2026 - 18:46

288

Views

Number of zeros of $p(z)=z^5+10z-3$ on annulus $A(0,1,2)$

Published on 15 Apr 2026 - 8:11

86

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non-existence of a polynomial

Published on 11 Apr 2026 - 10:14

768

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Zeroes of $\sin(z)-z^2$

Published on 16 Apr 2026 - 9:31

399

Views

Show that $z^5 - z +16$ has two roots in the right half plane

Published on 16 Apr 2026 - 12:47

234

Views

Inverse statement to Rouché's theorem in complex analysis.

Published on 09 Apr 2026 - 16:54

115

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$Re(\frac{f}{g})\geq 0$ on the boundary of disk implies $f$ and $g$ have same number of zeros in the disk

Published on 16 Apr 2026 - 6:30

62

Views

Bound on constant in Polynomial so that zeros are bounded (Rouche)

Published on 12 Apr 2026 - 0:55

List Question

Rouché's Theorem/Argument Principle Application

Finding number of roots to an equation

Showing that, for $|a|>3$ and $n\geq1$, the function $f(z)=e^z-az^n$ has exactly $n$ roots (all simple and different) in the open unit disc

Using Rouché's theorem to bound zeroes of partial sums of $e^z$

Prove that $ze^{\lambda - z} - 1$ has a real root in the unit disk

Roots of $z \sin(z) =1$

Solving non-homogeneous system of equations with Rouche Capelli theorem

Confusion in the proof of Rouché's theorem (joint continuity part)

Number of zeros of $p(z)=z^5+10z-3$ on annulus $A(0,1,2)$

non-existence of a polynomial

Zeroes of $\sin(z)-z^2$

Show that $z^5 - z +16$ has two roots in the right half plane

Inverse statement to Rouché's theorem in complex analysis.

$Re(\frac{f}{g})\geq 0$ on the boundary of disk implies $f$ and $g$ have same number of zeros in the disk

Bound on constant in Polynomial so that zeros are bounded (Rouche)

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