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Math Help - Conformality

  1. #1
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    Conformality

    1) Can anyone think of a function of a complex variable which is conformal at some points but not at others? Please indicate the point/s at which it is not conformal and the points at which it is.

    2) Consider a function of a complex variable and a point a in its domain. Can anyone think of a mapping which preserves angles between two particular curves intersecting at a but for which angle preservation does not occur for all pairs of curves intersecting at the same point a ?
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  2. #2
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    Quote Originally Posted by Ian Moore View Post
    1) Can anyone think of a function of a complex variable which is conformal at some points but not at others? Please indicate the point/s at which it is not conformal and the points at which it is.
    f(z)=z^2.

    2) Consider a function of a complex variable and a point a in its domain. Can anyone think of a mapping which preserves angles between two particular curves intersecting at a but for which angle preservation does not occur for all pairs of curves intersecting at the same point a ?
    Same function works.
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  3. #3
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    In "1) Can anyone think of a function of a complex variable which is conformal at some points but not at others? Please indicate the point/s at which it is not conformal and the points at which it is " I should have been more precise. I am after a non-analytic function satisfying the requirements previously outlined.

    In "2) Consider a function of a complex variable and a point a in its domain. Can anyone think of a mapping which preserves angles between two particular curves intersecting at a but for which angle preservation does not occur for all pairs of curves intersecting at the same point a ? I should have added here, Can you give an example of a point and of a pair of curves for which angle preservation holds as well as an example of a pair of curves through the same point where angle preservation does not occur.
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  4. #4
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    In that case use f(z) = |z|^2
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  5. #5
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    Thankyou Perfect Hacker.
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