Question

Prove that sufficiently large partial sums of the Taylor series expansion of $e^z$ have all roots outside of an arbitrarily large radius.

score 179 · Answer 1 · 2018-07-25 17:27:56

179

Views

Prove that sufficiently large partial sums of the Taylor series expansion of $e^z$ have all roots outside of an arbitrarily large radius.

Published on 25 Jul 2018 - 17:27

score 164 · Answer 2 · 2018-08-07 17:11:03

164

Views

how many roots does $p(z) = z^{10} + 100z + 1$ in $\{z:|z|<1\}$

Published on 07 Aug 2018 - 17:11

score 1.6k · Answer 3 · 2026-03-24 19:01:23

1.6k

Views

How many zeros does the polynomial have in the right half plane?

Published on 24 Mar 2026 - 19:01

score 86 · Answer 4 · 2018-08-09 13:52:04

86

Views

Using Rouché's theorem to prove the degree of a polynomial over $\mathbb{C}$

Published on 09 Aug 2018 - 13:52

score 624 · Answer 5 · 2018-08-14 23:40:56

624

Views

Finding the number of zeros of a polynomial in the closed disk

Published on 14 Aug 2018 - 23:40

score 154 · Answer 6 · 2018-09-16 21:56:31

154

Views

Application of Rouché's theorem outside the unit circle; Confusion about argument principle

Published on 16 Sep 2018 - 21:56

score 39 · Answer 7 · 2018-10-07 18:34:35

39

Views

Find number of elements $z$, $1<|z|<2$ satisfying $f(z)=0$ where $f(z)=z^5+z^3+5z^2+2$.

Published on 07 Oct 2018 - 18:34

score 1.3k · Answer 8 · 2018-10-15 02:25:33

1.3k

Views

Show that $f_a(z)=z+a-e^z$ has only 1 zero in $Re(z)<0$ and this zero is $<0$. $(a>1)$

Published on 15 Oct 2018 - 2:25

score 167 · Answer 9 · 2018-10-28 19:51:24

167

Views

Number of solutions of $z^5+4z^3=e^{iz}$ in $A=\{z:1 < |z| < 3\}.$

Published on 28 Oct 2018 - 19:51

score 373 · Answer 10 · 2018-11-03 01:52:25

373

Views

Question on Rouche's Theorem - Boundary Included?

Published on 03 Nov 2018 - 1:52

score 316 · Answer 11 · 2018-11-09 01:54:54

316

Views

If $11z^8+20iz^7+10iz-22=0$,then show that $1<|z|<2$

Published on 09 Nov 2018 - 1:54

score 768 · Answer 12 · 2018-12-14 12:50:19

768

Views

Rouche's theorem in the right half plane

Published on 14 Dec 2018 - 12:50

score 473 · Answer 13 · 2018-12-17 22:10:23

473

Views

Find the number of zeros of $f(z)=e^{z-1}-az$ inside unit disk, assuming $\mid a \mid >1$

Published on 17 Dec 2018 - 22:10

score 1.8k · Answer 14 · 2018-12-18 21:49:45

1.8k

Views

How many roots does $g(z)=z^7-2z^5+6z^3-z+1$ have inside the unit disk - Rouche's Theorem Application Verification

Published on 18 Dec 2018 - 21:49

score 123 · Answer 15 · 2018-12-21 14:58:21

123

Views

finding the number of solutions $9z^4=\sin^2(z)$ in a complex sector

Published on 21 Dec 2018 - 14:58

List Question

Prove that sufficiently large partial sums of the Taylor series expansion of $e^z$ have all roots outside of an arbitrarily large radius.

how many roots does $p(z) = z^{10} + 100z + 1$ in $\{z:|z|<1\}$

How many zeros does the polynomial have in the right half plane?

Using Rouché's theorem to prove the degree of a polynomial over $\mathbb{C}$

Finding the number of zeros of a polynomial in the closed disk

Application of Rouché's theorem outside the unit circle; Confusion about argument principle

Find number of elements $z$, $1<|z|<2$ satisfying $f(z)=0$ where $f(z)=z^5+z^3+5z^2+2$.

Show that $f_a(z)=z+a-e^z$ has only 1 zero in $Re(z)<0$ and this zero is $<0$. $(a>1)$

Number of solutions of $z^5+4z^3=e^{iz}$ in $A=\{z:1 < |z| < 3\}.$

Question on Rouche's Theorem - Boundary Included?

If $11z^8+20iz^7+10iz-22=0$,then show that $1<|z|<2$

Rouche's theorem in the right half plane

Find the number of zeros of $f(z)=e^{z-1}-az$ inside unit disk, assuming $\mid a \mid >1$

How many roots does $g(z)=z^7-2z^5+6z^3-z+1$ have inside the unit disk - Rouche's Theorem Application Verification

finding the number of solutions $9z^4=\sin^2(z)$ in a complex sector

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