(l) The points 1 +3. 5 + 21 and 2 + 33 form the vertices of a scalene triangle when located on an Argand diagram in the complex z-plane. Using the relation = 55- ' 2*d2, where A is the area, C the contour traversed along the triangle perimeter, and z = 1+Jy determine the area of the triangle. Verify your answer by using the standard formula for the area of any triangle by calculating the length of its sides. (2) A circular arc of radius a subtends an angle of 0 at the origin of the coordinates in the complex z-plane. Using the formula given in problem # 1. show that the area under the circular arc is #29, where 0 is measured in radians. (3) Consider the complex function w(z) =n(rr, y)+;v(:r, y). Prove that if V x Viv = 0, then either w(z) is real or that Sm(w(z))=v(r,y) is a harmonic function. (4) Prove that hzz') is not analytic anywhere in the complex plane. (5) If u(a:, y) and v(:. y) are harmonic functions in a region R, then prove that e41!) + me By 3:: J(Star y is an analytic function anywhere in the complex plane