Transformation of line with fractional linear transformation
$begingroup$
Let $T(z) = ifrac{z+1}{z-1}$, for $zinmathbb{C}$.
How do I complete the following statement:
$Linmathbb{C}$ is a line such that $T(Lcup{infty})=L'cup{infty}$ where $L'$ is a line if and only if...
I understand that $T(infty)=i$ and $T(1)=infty$. I have computed the inverse too: it's $T^{-1}(z)=frac{z+i}{z-i}$.
I don't really get how to get the answer to the question. What is even a line with a point at infinity?...
complex-analysis geometry
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
$endgroup$
add a comment |
$begingroup$
Let $T(z) = ifrac{z+1}{z-1}$, for $zinmathbb{C}$.
How do I complete the following statement:
$Linmathbb{C}$ is a line such that $T(Lcup{infty})=L'cup{infty}$ where $L'$ is a line if and only if...
I understand that $T(infty)=i$ and $T(1)=infty$. I have computed the inverse too: it's $T^{-1}(z)=frac{z+i}{z-i}$.
I don't really get how to get the answer to the question. What is even a line with a point at infinity?...
complex-analysis geometry
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
$endgroup$
$begingroup$
The question doesn't use the convention that every straight line goes through the point at infinity, saying "a straight line plus the point at infinity" instead. The question is just this: which straight lines are mapped to straight lines rather than to circles by $T$?
$endgroup$
– Maxim
Jan 13 at 22:10
add a comment |
$begingroup$
Let $T(z) = ifrac{z+1}{z-1}$, for $zinmathbb{C}$.
How do I complete the following statement:
$Linmathbb{C}$ is a line such that $T(Lcup{infty})=L'cup{infty}$ where $L'$ is a line if and only if...
I understand that $T(infty)=i$ and $T(1)=infty$. I have computed the inverse too: it's $T^{-1}(z)=frac{z+i}{z-i}$.
I don't really get how to get the answer to the question. What is even a line with a point at infinity?...
complex-analysis geometry
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
$endgroup$
Let $T(z) = ifrac{z+1}{z-1}$, for $zinmathbb{C}$.
How do I complete the following statement:
$Linmathbb{C}$ is a line such that $T(Lcup{infty})=L'cup{infty}$ where $L'$ is a line if and only if...
I understand that $T(infty)=i$ and $T(1)=infty$. I have computed the inverse too: it's $T^{-1}(z)=frac{z+i}{z-i}$.
I don't really get how to get the answer to the question. What is even a line with a point at infinity?...
complex-analysis geometry
complex-analysis geometry
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
asked Jan 13 at 17:42
AstlyDichrarAstlyDichrar
42248
42248
$begingroup$
The question doesn't use the convention that every straight line goes through the point at infinity, saying "a straight line plus the point at infinity" instead. The question is just this: which straight lines are mapped to straight lines rather than to circles by $T$?
$endgroup$
– Maxim
Jan 13 at 22:10
add a comment |
$begingroup$
The question doesn't use the convention that every straight line goes through the point at infinity, saying "a straight line plus the point at infinity" instead. The question is just this: which straight lines are mapped to straight lines rather than to circles by $T$?
$endgroup$
– Maxim
Jan 13 at 22:10
$begingroup$
The question doesn't use the convention that every straight line goes through the point at infinity, saying "a straight line plus the point at infinity" instead. The question is just this: which straight lines are mapped to straight lines rather than to circles by $T$?
$endgroup$
– Maxim
Jan 13 at 22:10
$begingroup$
The question doesn't use the convention that every straight line goes through the point at infinity, saying "a straight line plus the point at infinity" instead. The question is just this: which straight lines are mapped to straight lines rather than to circles by $T$?
$endgroup$
– Maxim
Jan 13 at 22:10
add a comment |
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$begingroup$
The question doesn't use the convention that every straight line goes through the point at infinity, saying "a straight line plus the point at infinity" instead. The question is just this: which straight lines are mapped to straight lines rather than to circles by $T$?
$endgroup$
– Maxim
Jan 13 at 22:10