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Complex Analysis
Find the image of (the region outside the unite circle |z| = 1 and between the ray arg(z) = pi/4 and
arg(z) = 3pi/4 ) under the mapping w = Ln z
Solution
w= ln z
pi/41
z = x+iy where x^2+y^2 >1 andtan y/x lies between -1 and +1
ln z = ln(x+iy) for x,y such tht x^2+y^2 >1 andtan y/x lies between -1 and +1
x = r cost, y =rsint, r >1 and pi/4

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Complex AnalysisFind the image of (the region outside the unite ci.pdf

  • 1. Complex Analysis Find the image of (the region outside the unite circle |z| = 1 and between the ray arg(z) = pi/4 and arg(z) = 3pi/4 ) under the mapping w = Ln z Solution w= ln z pi/41 z = x+iy where x^2+y^2 >1 andtan y/x lies between -1 and +1 ln z = ln(x+iy) for x,y such tht x^2+y^2 >1 andtan y/x lies between -1 and +1 x = r cost, y =rsint, r >1 and pi/4