Question

Find the number of roots of the polynomial $P(z)=z^5+2z^3+3$ in the closed unit disk $\{z\colon |z|\le 1\}$.

score 191 · Answer 1 · 2026-04-16 13:12:16

191

Views

Find the number of roots of the polynomial $P(z)=z^5+2z^3+3$ in the closed unit disk $\{z\colon |z|\le 1\}$.

Published on 16 Apr 2026 - 13:12

score 120 · Answer 2 · 2026-04-09 01:53:36

120

Views

Can you help on complex analysis problem

Published on 09 Apr 2026 - 1:53

score 126 · Answer 3 · 2026-04-16 01:16:12

126

Views

Applying Rouché's theorem in a square

Published on 16 Apr 2026 - 1:16

score 252 · Answer 4 · 2026-04-12 03:03:08

252

Views

rouche's theorem without strict inequality

Published on 12 Apr 2026 - 3:03

score 998 · Answer 5 · 2026-03-25 03:07:28

998

Views

show $\frac{z}{(1+z)^2}$ is injective in the unit disk

Published on 25 Mar 2026 - 3:07

score 77 · Answer 6 · 2026-03-25 04:34:58

77

Views

Prove given function is not injective

Published on 25 Mar 2026 - 4:34

score 61 · Answer 7 · 2026-03-25 03:07:53

61

Views

Which of the following is true?[Using Formal approach]

Published on 25 Mar 2026 - 3:07

score 200 · Answer 8 · 2026-03-25 04:39:21

200

Views

Roots of a polynomial on the unit circle

Published on 25 Mar 2026 - 4:39

score 54 · Answer 9 · 2026-03-25 04:43:38

54

Views

Find the number of zeroes of a function $z^3+z^2 +z+1$ lying inside $|z|=2$ by Rouche's theorem?

Published on 25 Mar 2026 - 4:43

score 189 · Answer 10 · 2026-03-25 03:03:16

189

Views

Non-real roots of $z^2=\sin(z)$

Published on 25 Mar 2026 - 3:03

score 326 · Answer 11 · 2026-03-25 04:41:37

326

Views

Compute the roots of $z^{5}-4z^{3}+6=0$ in the closed first quadrant

Published on 25 Mar 2026 - 4:41

score 1k · Answer 12 · 2026-03-25 03:03:55

1k

Views

Show that the equation $e^z=az^n$ has $n$ solutions in the unit disc centred at the origin counting multiplicity.

Published on 25 Mar 2026 - 3:03

score 262 · Answer 13 · 2026-03-25 03:03:50

262

Views

Showing $1-2z^2-2z^3-2z^4-2z^5$ has a unique root inside the disk of radius 0.6

Published on 25 Mar 2026 - 3:03

score 210 · Answer 14 · 2026-03-25 03:02:39

210

Views

Rouché's Theorem with $h(z)=z^3+8z+23$

Published on 25 Mar 2026 - 3:02

score 177 · Answer 15 · 2026-03-25 03:01:41

177

Views

Number of zeros inside and outside unit disc

Published on 25 Mar 2026 - 3:01

List Question

Find the number of roots of the polynomial $P(z)=z^5+2z^3+3$ in the closed unit disk $\{z\colon |z|\le 1\}$.

Can you help on complex analysis problem

Applying Rouché's theorem in a square

rouche's theorem without strict inequality

show $\frac{z}{(1+z)^2}$ is injective in the unit disk

Prove given function is not injective

Which of the following is true?[Using Formal approach]

Roots of a polynomial on the unit circle

Find the number of zeroes of a function $z^3+z^2 +z+1$ lying inside $|z|=2$ by Rouche's theorem?

Non-real roots of $z^2=\sin(z)$

Compute the roots of $z^{5}-4z^{3}+6=0$ in the closed first quadrant

Show that the equation $e^z=az^n$ has $n$ solutions in the unit disc centred at the origin counting multiplicity.

Showing $1-2z^2-2z^3-2z^4-2z^5$ has a unique root inside the disk of radius 0.6

Rouché's Theorem with $h(z)=z^3+8z+23$

Number of zeros inside and outside unit disc

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