There are five problems in this assignment. Answer all the problems.
problem 1: (i) Find the complex conjugate of (3+5i)/(1+2i)
(ii) Differentiate (sin x)x w.r.t. x.
(iii) Find all the seventh roots of (3+4i).
problem 2: (i) Find the equation of the line joining the points (-, 6, - 3) and (7, - 6, 3).
(ii) Find the equation of the sphere, which contains the circle
x2 + y2 + z2 = 18 , 3x + 3y + 3z = 11 and passes through the origin.
problem 3: (i) Find lim 1+x2/x2
x → ∞
(ii) Compute the area bounded by y2 = 9x and x2 = 9y
(iii) Evaluate: ∫tan^{-1} x dx
problem 4: Use the Cauchy - Schwarz inequality to solve x^{3} - 25x^{2} - 4x + 100 = 0, given that all its roots are rational.
problem 5: (i) Find the perimeter of the cord r = a (1 + cos θ)
(ii) Find all the seventh roots of (3+4i).