Q1-State and prove Liouville's theorem. Q2- Show that fo loge x (1+x2)2 4 100 Q2-Prove that cosh (z+ ) = a + m 1 an (z" + ). Where a n=1 1 Q4- Prove that Cauchy's integral formula f(a) = f(z) dz - -- z-a 1 2 = cosh 0 cosh(2 cos 0)de. Q5- Prove that all roots of z 5z + 12 = 0 lies between the circle | z| = 1 circle |z| = 2