how many roots does $p(z) = z^10 + 100z + 1$ in $|z<1|$
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how many roots does $p(z) = z^10 + 100z + 1$ has in $|z<1|$
Can I use Rouche theorem and say that on that region $|100z|=100>2=1+1=|z^10|+1$
and thus the number of roots for p(z) is the same as the number of roots for $100z$ which is $1$ (the root is $0$)?
is it that simple?
complex-analysis polynomials rouches-theorem
asked Aug 7 at 17:11
SlyxBrd
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favorite
how many roots does $p(z) = z^10 + 100z + 1$ has in $|z<1|$
Can I use Rouche theorem and say that on that region $|100z|=100>2=1+1=|z^10|+1$
and thus the number of roots for p(z) is the same as the number of roots for $100z$ which is $1$ (the root is $0$)?
is it that simple?
complex-analysis polynomials rouches-theorem
asked Aug 7 at 17:11
SlyxBrd
295
What does $|z<1|$ mean?And why is $|100z| = 100$???
– amsmath
Aug 7 at 17:12
If Nerval circles a tree one time, always keeping a distance of 100 units, and is leash is 2 units, then his lobster walks around the tree one time.
– Doug M
Aug 7 at 17:27
Yes, it is that simple, but you should clean up the solution a bit. It is not so that "on that region" ($|z|<1$) $100|z|=100$ nor that $|z^10|+1=2$ This is true on the boundary of the region.
– saulspatz
Aug 7 at 17:34
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
how many roots does $p(z) = z^10 + 100z + 1$ has in $|z<1|$
Can I use Rouche theorem and say that on that region $|100z|=100>2=1+1=|z^10|+1$
and thus the number of roots for p(z) is the same as the number of roots for $100z$ which is $1$ (the root is $0$)?
is it that simple?
complex-analysis polynomials rouches-theorem
asked Aug 7 at 17:11
SlyxBrd
295
how many roots does $p(z) = z^10 + 100z + 1$ has in $|z<1|$
Can I use Rouche theorem and say that on that region $|100z|=100>2=1+1=|z^10|+1$
and thus the number of roots for p(z) is the same as the number of roots for $100z$ which is $1$ (the root is $0$)?
is it that simple?
complex-analysis polynomials rouches-theorem
asked Aug 7 at 17:11
SlyxBrd
295
asked Aug 7 at 17:11
SlyxBrd
295
asked Aug 7 at 17:11
SlyxBrd
295
asked Aug 7 at 17:11
SlyxBrd
295
295
What does $|z<1|$ mean?And why is $|100z| = 100$???
– amsmath
Aug 7 at 17:12
If Nerval circles a tree one time, always keeping a distance of 100 units, and is leash is 2 units, then his lobster walks around the tree one time.
– Doug M
Aug 7 at 17:27
Yes, it is that simple, but you should clean up the solution a bit. It is not so that "on that region" ($|z|<1$) $100|z|=100$ nor that $|z^10|+1=2$ This is true on the boundary of the region.
– saulspatz
Aug 7 at 17:34
add a comment |Â
What does $|z<1|$ mean?And why is $|100z| = 100$???
– amsmath
Aug 7 at 17:12
If Nerval circles a tree one time, always keeping a distance of 100 units, and is leash is 2 units, then his lobster walks around the tree one time.
– Doug M
Aug 7 at 17:27
Yes, it is that simple, but you should clean up the solution a bit. It is not so that "on that region" ($|z|<1$) $100|z|=100$ nor that $|z^10|+1=2$ This is true on the boundary of the region.
– saulspatz
Aug 7 at 17:34
What does $|z<1|$ mean?And why is $|100z| = 100$???
– amsmath
Aug 7 at 17:12
What does $|z<1|$ mean?And why is $|100z| = 100$???
– amsmath
Aug 7 at 17:12
If Nerval circles a tree one time, always keeping a distance of 100 units, and is leash is 2 units, then his lobster walks around the tree one time.
– Doug M
Aug 7 at 17:27
If Nerval circles a tree one time, always keeping a distance of 100 units, and is leash is 2 units, then his lobster walks around the tree one time.
– Doug M
Aug 7 at 17:27
Yes, it is that simple, but you should clean up the solution a bit. It is not so that "on that region" ($|z|<1$) $100|z|=100$ nor that $|z^10|+1=2$ This is true on the boundary of the region.
– saulspatz
Aug 7 at 17:34
Yes, it is that simple, but you should clean up the solution a bit. It is not so that "on that region" ($|z|<1$) $100|z|=100$ nor that $|z^10|+1=2$ This is true on the boundary of the region.
– saulspatz
Aug 7 at 17:34
add a comment |Â
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What does $|z<1|$ mean?And why is $|100z| = 100$???
– amsmath
Aug 7 at 17:12
If Nerval circles a tree one time, always keeping a distance of 100 units, and is leash is 2 units, then his lobster walks around the tree one time.
– Doug M
Aug 7 at 17:27
Yes, it is that simple, but you should clean up the solution a bit. It is not so that "on that region" ($|z|<1$) $100|z|=100$ nor that $|z^10|+1=2$ This is true on the boundary of the region.
– saulspatz
Aug 7 at 17:34