answer please

Section-A 1) Suppose w = =. Without doing any calculations, explain why |wl = 1 2) What can be said about complex number z if z = z? If (z)? = (z)2 3) Student A states that, even though she cant find it in the text, she thinks that arg(2) = - arg(z) . For example, she says, if = = 1 + i, then = = 1 - i and arg(=) and arg (3) = - 4 Student B disagrees because he feels that he has a counter example: if = = i and z 317 = -i; we can take arg(i) = = and arg(-1) = - and so arg(i) # - arg(-1) . Take sides and defend your position. 4) Define removable singuarities and pole. 5) Evaluate S. (63 + 4) dz where C is the straight line from 1 + i to 2 + 3i. 6) For any complex number. = = 0. evaluate ="Section-B 1) Use es = ex cosy + ie* sin y to prove that = = =1 - 852. 2) If | sin z)