11. Let a and b be distinct complex numbers and 0 < α < π . (i) When z 1 lies on the circular arc shown, it subtends a constant angle α . This angle is given by Arg( z 1-a )-Arg( z 1-b ). However Arg µ z 1-a z 1-b ¶ = Arg( z 1-a )-Arg( z 1-b ) + 2 kπ = α + 2 kπ. It follows that k = 0, as 0 < α < π and-π < Arg θ ≤ π . Hence Arg µ z 1-a z 1-b ¶ = α. Similarly if z 2 lies on the circular arc shown, then Arg µ z 2-a z 2-b ¶ =-γ =
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This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.