Complex analysis: Please help me with 3 & 4. Problem 2 is quite straightforward.

Consider the two following curves. Curve 71 consists of the line segment from the origin to R {on the real mos}T followed by the arc to Hi {on the imaginary axis}, then the line segment back to the origin. Curve 1-; consists of the line segment from the origin to 11R, followed by the arc to R, then the line segment back to the origin. Curves 73 and 71 are illustrated below. 2. Explain why the sum of the integrals along 72 and y1 give the original integral around the semicircle , i.e. piwz elwz elwz plwz 24 + 1 dz + dz = in dz + dz. 24 + 1 2* + 1 are 24 + 1 The upshot of this is that we can compute these two integrals. 3. Use the Cauchy Integral Formula to show that (for R large enough so that the singular points at z = Alti V2 are enclosed by the relevant curve): piwz iw (1+ dz = 2xi 16 -w/ V2 1( y-4) 24+1 4( V2 and plwz dz = 2mi IT -w/v2-i(#-1) 24 + 1 4( 1+ (Hint: 24 +1 = (2 - 1#1)(2 - 1-)(2 - =1#) ( - =), and 1ti = exit, and =1ti = exit) 4. Hence deduce piut w -dt = Te Vi cos 14 + 1 12