What is complex number & conjugate complex number? Prove that the sum and product of two complex number and conjugate complex number is real. 1. 2. Find the modulus and argument of the complex number (2. Also express -5 + 5i in polar form. 3. What is analytic function? Show that u = 3x?y + 2x2 - y3 2y? is a harmonic function. 4. If x = cose + isin0 & 1 + V1 a? = na then prove that 1 + acos0 = (1+ nx)(1+) a 2n