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We are working on functions of complex variables in calculus (Chpt. 17.4 in Advanced Engineering Mathematics),...

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Advance Math

We are working on functions of complex variables in calculus(Chpt. 17.4 in Advanced Engineering Mathematics), and our profposed us the following question:

\"Find the function w = u + iv = f(z) that maps the region S :={z : 0 ≤ arg z ≤ π 4 } to the upper half plane {w = u + iv : v ≥0}.\"

the answer he gave to this problem was as follows: \"such amapping is given by f(z) = z^4 = r^4*e^4iθ where z = re^iθ .\"

I am unsure how he came to this conclusion, could someone pleasehelp? Thanks!

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