Plotting Reciprocal of a Complex inequality
We have a complex inequality $|z-r|leq{sqrt{r}}$. (${r>0}$ is a real constant number and $z$ is a variable complex number). Now we want to find the plot of $f(z) = 1/z$ where $z$ are the answers of above inequality. i.e. we want to find plot of: $|1/z-r|leq sqrt{r}$ $~~~$
I know that the first one is the plot of a circle with Radius $=sqrt r$ and center is $r + 0 i$. (All the point inside and on the perimeter of circle).
But I don't know what to do with the reciprocal of $z$ in $|1/z-r|leq sqrt{r}$ .
complex-numbers graphing-functions
asked Nov 28 '18 at 20:10
amir na
385
add a comment |
We have a complex inequality $|z-r|leq{sqrt{r}}$. (${r>0}$ is a real constant number and $z$ is a variable complex number). Now we want to find the plot of $f(z) = 1/z$ where $z$ are the answers of above inequality. i.e. we want to find plot of: $|1/z-r|leq sqrt{r}$ $~~~$
I know that the first one is the plot of a circle with Radius $=sqrt r$ and center is $r + 0 i$. (All the point inside and on the perimeter of circle).
But I don't know what to do with the reciprocal of $z$ in $|1/z-r|leq sqrt{r}$ .
complex-numbers graphing-functions
asked Nov 28 '18 at 20:10
amir na
385
add a comment |
We have a complex inequality $|z-r|leq{sqrt{r}}$. (${r>0}$ is a real constant number and $z$ is a variable complex number). Now we want to find the plot of $f(z) = 1/z$ where $z$ are the answers of above inequality. i.e. we want to find plot of: $|1/z-r|leq sqrt{r}$ $~~~$
I know that the first one is the plot of a circle with Radius $=sqrt r$ and center is $r + 0 i$. (All the point inside and on the perimeter of circle).
But I don't know what to do with the reciprocal of $z$ in $|1/z-r|leq sqrt{r}$ .
complex-numbers graphing-functions
asked Nov 28 '18 at 20:10
amir na
385
We have a complex inequality $|z-r|leq{sqrt{r}}$. (${r>0}$ is a real constant number and $z$ is a variable complex number). Now we want to find the plot of $f(z) = 1/z$ where $z$ are the answers of above inequality. i.e. we want to find plot of: $|1/z-r|leq sqrt{r}$ $~~~$
I know that the first one is the plot of a circle with Radius $=sqrt r$ and center is $r + 0 i$. (All the point inside and on the perimeter of circle).
But I don't know what to do with the reciprocal of $z$ in $|1/z-r|leq sqrt{r}$ .
complex-numbers graphing-functions
complex-numbers graphing-functions
asked Nov 28 '18 at 20:10
amir na
385
asked Nov 28 '18 at 20:10
amir na
385
asked Nov 28 '18 at 20:10
amir na
385
asked Nov 28 '18 at 20:10
amir na
385
asked Nov 28 '18 at 20:10
amir na
385
385
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Let $D$ be the unit disc, then your original inequality is satisfied by is the set
$$
r + zsqrt{r}, quad z in D
$$
and the inverse would be
$$
frac{1}{r+zsqrt{r}}, quad z in D.
$$
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
Can you say what will be the shape of $frac{1}{r+zsqrt{r}}, quad z in D$ if we graph it? The question is maybe "what is reciprocal of a circle?".
– amir na
Nov 28 '18 at 20:19
@amirna why don't you do some work on this problem as well? Map out the image of the 4 extremes of the circle under the transformation and perhaps you will get some idea
– gt6989b
Nov 28 '18 at 20:21
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Let $D$ be the unit disc, then your original inequality is satisfied by is the set
$$
r + zsqrt{r}, quad z in D
$$
and the inverse would be
$$
frac{1}{r+zsqrt{r}}, quad z in D.
$$
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
Can you say what will be the shape of $frac{1}{r+zsqrt{r}}, quad z in D$ if we graph it? The question is maybe "what is reciprocal of a circle?".
– amir na
Nov 28 '18 at 20:19
@amirna why don't you do some work on this problem as well? Map out the image of the 4 extremes of the circle under the transformation and perhaps you will get some idea
– gt6989b
Nov 28 '18 at 20:21
add a comment |
Let $D$ be the unit disc, then your original inequality is satisfied by is the set
$$
r + zsqrt{r}, quad z in D
$$
and the inverse would be
$$
frac{1}{r+zsqrt{r}}, quad z in D.
$$
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
Can you say what will be the shape of $frac{1}{r+zsqrt{r}}, quad z in D$ if we graph it? The question is maybe "what is reciprocal of a circle?".
– amir na
Nov 28 '18 at 20:19
@amirna why don't you do some work on this problem as well? Map out the image of the 4 extremes of the circle under the transformation and perhaps you will get some idea
– gt6989b
Nov 28 '18 at 20:21
add a comment |
Let $D$ be the unit disc, then your original inequality is satisfied by is the set
$$
r + zsqrt{r}, quad z in D
$$
and the inverse would be
$$
frac{1}{r+zsqrt{r}}, quad z in D.
$$
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
Let $D$ be the unit disc, then your original inequality is satisfied by is the set
$$
r + zsqrt{r}, quad z in D
$$
and the inverse would be
$$
frac{1}{r+zsqrt{r}}, quad z in D.
$$
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
answered Nov 28 '18 at 20:16
gt6989b
33.1k22452
33.1k22452
Can you say what will be the shape of $frac{1}{r+zsqrt{r}}, quad z in D$ if we graph it? The question is maybe "what is reciprocal of a circle?".
– amir na
Nov 28 '18 at 20:19
@amirna why don't you do some work on this problem as well? Map out the image of the 4 extremes of the circle under the transformation and perhaps you will get some idea
– gt6989b
Nov 28 '18 at 20:21
add a comment |
Can you say what will be the shape of $frac{1}{r+zsqrt{r}}, quad z in D$ if we graph it? The question is maybe "what is reciprocal of a circle?".
– amir na
Nov 28 '18 at 20:19
@amirna why don't you do some work on this problem as well? Map out the image of the 4 extremes of the circle under the transformation and perhaps you will get some idea
– gt6989b
Nov 28 '18 at 20:21
Can you say what will be the shape of $frac{1}{r+zsqrt{r}}, quad z in D$ if we graph it? The question is maybe "what is reciprocal of a circle?".
– amir na
Nov 28 '18 at 20:19
Can you say what will be the shape of $frac{1}{r+zsqrt{r}}, quad z in D$ if we graph it? The question is maybe "what is reciprocal of a circle?".
– amir na
Nov 28 '18 at 20:19
@amirna why don't you do some work on this problem as well? Map out the image of the 4 extremes of the circle under the transformation and perhaps you will get some idea
– gt6989b
Nov 28 '18 at 20:21
@amirna why don't you do some work on this problem as well? Map out the image of the 4 extremes of the circle under the transformation and perhaps you will get some idea
– gt6989b
Nov 28 '18 at 20:21
add a comment |
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