List questions from rouches-theorem

Published on 16 Apr 2026 - 8:03

133

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Show that $f$ has exactly two zeros (counting multiplicity)

Published on 13 Apr 2026 - 4:36

159

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Show that $f$ has exactly one zero on the square $Q =$ {$x + iy ∈ \Bbb C : |x| < 1, |y| < 1$}.

Published on 17 Apr 2026 - 6:26

59

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Using Rouché's theorem to find zeros

Published on 14 Apr 2026 - 4:46

107

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If $f$ is analytic on $\overline{B(0,1)}$, and $|f(z)| < 1$ for $|z|=1$. Find the number of solutions to $f(z) = z^n$

Published on 15 Apr 2026 - 3:58

113

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Inequality of $|e^z - 1|$

Published on 30 Apr 2026 - 14:06

85

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An application of Rouché's theorem

Published on 08 Apr 2026 - 23:29

78

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Rouché's theorem for $|z|>2$

Published on 13 Apr 2026 - 2:42

389

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Rouché's theorem in annulus $1<|z|<2$

Published on 15 Apr 2026 - 17:32

30

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Given $f\in Hol(|z|<1)$ and $image(f(z))\subset K\subset D_0(1)$ where K is compact subset Prove that $f$ has one fixed point.

Published on 16 Apr 2026 - 1:38

137

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Show that all of the roots of $f(z)= cz^n-e^z$ are from multiplicity of 1

Published on 15 Apr 2026 - 20:49

191

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Rouché's theorem, and distinct zeroes.

Published on 16 Apr 2026 - 0:59

48

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Yet another Rouché's theorem example for $f(z) = e^z-3z^{2019}$ - solution verification

Published on 14 Apr 2026 - 10:27

244

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Rouché's Theorem on $f_n(z)=1+\frac{1}{z}+\dots +\frac{1}{n!z^n}$

Published on 17 Apr 2026 - 14:44

559

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Using Rouche's Theorem to find the number of solutions of $f(z)=z$ in the open unit disc

Published on 14 Apr 2026 - 2:31

List Question

Zeroes of $2z^5-15z^2+z+2$

Show that $f$ has exactly two zeros (counting multiplicity)

Show that $f$ has exactly one zero on the square $Q =$ {$x + iy ∈ \Bbb C : |x| < 1, |y| < 1$}.

Using Rouché's theorem to find zeros

If $f$ is analytic on $\overline{B(0,1)}$, and $|f(z)| < 1$ for $|z|=1$. Find the number of solutions to $f(z) = z^n$

Inequality of $|e^z - 1|$

An application of Rouché's theorem

Rouché's theorem for $|z|>2$

Rouché's theorem in annulus $1<|z|<2$

Given $f\in Hol(|z|<1)$ and $image(f(z))\subset K\subset D_0(1)$ where K is compact subset Prove that $f$ has one fixed point.

Show that all of the roots of $f(z)= cz^n-e^z$ are from multiplicity of 1

Rouché's theorem, and distinct zeroes.

Yet another Rouché's theorem example for $f(z) = e^z-3z^{2019}$ - solution verification

Rouché's Theorem on $f_n(z)=1+\frac{1}{z}+\dots +\frac{1}{n!z^n}$

Using Rouche's Theorem to find the number of solutions of $f(z)=z$ in the open unit disc

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