homework20110912

homework20110912 - z 7 5 z 3 + 1 /z b) f ( z ) = 2 z 3 z 1...

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Math 417, Fall 2011 Exercise Set #2 Turn in: September 12 1. Find the real and imaginary parts of the functions: a) f ( z )= z 1 z 2 b) f ( z )=exp(2 z +5 i ) c) f ( z )=3 z 2 +7 z i 2. Show (using the de±nition and properties of limits) that a) lim z 2 z 2 4 z 2 =4 . b) lim z →∞ 3 z 4 2 z 7 = 3 2 . c) lim z 2 z 3 z 2 = . 3. Find the derivatives of the following functions: a) f ( z
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Unformatted text preview: z 7 5 z 3 + 1 /z b) f ( z ) = 2 z 3 z 1 4. Consider a regular n-gon inscribed in the unit circle in the complex plane. Join one vertex of the n-gon to each of the other vertices by a line segment. Show that the product of the lengths of these line segments is n . 1...
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