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homework20110926

# homework20110926 - 5 Evaluate the integral ° π 6 e i 2 t...

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Math 417, Fall 2011 Exercise Set #4 Turn in: September 26 1. Log is the Principal Part of log, so Log ( z ) = ln( r ) + Θ , for π < Θ < π . Calculate: a) Log (1 + i ) b) Log ( ei ) c) log(1 i ) 2. Find all values of: a) 2 i b) (1 + i 3) 3 / 2 3. Prove the following formula involving trigonometric functions: | cos( z ) | 2 = cos 2 ( x ) + sinh 2 ( y ) , where z = x + i y 4. Solve the equation sin( z ) = 2 for z , by equating real and imaginary parts.
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Unformatted text preview: 5. Evaluate the integral: ° π/ 6 e i 2 t dt 6. Evaluate the contour integral, for the two contours given below: ° C z + 4 z dz a) C is the semi-circle z = 4 e iθ for 0 ≤ θ ≤ π . b) C is the circle z = 4 e iθ for 0 ≤ θ ≤ 2 π . 1...
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