Conformal Mappings :
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Angle between two curves at an intersecting point $\infty$: Two continuous curves $\gamma_{1}$ and $\gamma_{2}$ in the extended complex plane $\widehat{C}$ form an angle $\theta$ at an intersecting point $z = \infty$ if and only if their images $\gamma_{1}^{*}$ and $\gamma_{2}^{*}$ in the extended complex plane under the transformation $\zeta = 1 / z$ form an angle $\theta$ at the intersecting point $\zeta = 0$.

Angle between two curves at an intersecting point $\infty$: Two continuous curves $\gamma_{1}$ and $\gamma_{2}$ in the extended complex plane $\widehat{C}$ form an angle $\theta$ at an intersecting point $z = \infty$ if and only if their images $\gamma_{1}^{*}$ and $\gamma_{2}^{*}$ in the extended complex plane under the transformation $\zeta = 1 / z$ form an angle $\theta$ at the intersecting point $\zeta = 0$.

Example: The angle between the real and imaginary axes at $z=\infty$ is $\pi /2$ since the angle between the image curves of the real and imaginary axes under $\zeta = 1 / z$ at the point $\zeta = 0$.

The theorem of greatest importance in the subject of conformal mapping is the famous theorem of Bernhard Riemann.

 

  
 
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