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

We are working on functions of complex variables in calculus (Chpt. 17.4 in Advanced Engineering Mathematics), and our prof posed 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 a mapping 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 please help? Thanks!

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Expert Solution

Colby Messinger answered 1 year ago

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