solutions to this will be very helpful

3. (2 points) Write the following in the form ((2) = (x, y) + in(:c, y) where z = x + iy: (a) ((2) = 1/(2 i) (b) ((2) = (Z + 1)/(Z 1) Note that Z is the complex conjugate of z. 4. (4 points) Find and classify all of the singularities in the nite complex zplane for each of the following func tions: (a) f(z) = (4+ 22)/(4 22) (b) f(2) = (4 + 22)/(4 z)2 5. (6 points) Consider the contour integral 1 d 6 42225224 z () where the contour C is the unit circle. Let z = 6m and show that this integral is the same as: 27r 1 d6 7 /0 4sin0 5 ( ) Use the Residue Theorem to evaluate the contour integral and thereby nd the value of the second integral. Hint: sin0 = (6'0 616)/2'i