Question

Find the square of root(9+40i) + root(9-40i)​

Answer 1

Answer:

Let (x + iy)2 = 9 + 40i ∴ x2 – y2 = 9 ...............(i) and xy = 20 ...............(ii) squing (i) and adding with 4 times the square of (ii) we get x4 + y4 – 2x2 y2 + 4x2 y2 = 81 + 1600 ⇒ (x2 + y2)2 = 168 ⇒ x2 + y2 = 4 ...............(iii) from (i) + (iii) we get x2 = 25 ⇒ x = ± 5 and y = 16 ⇒ y = ± 4 from equation (ii) we can see that x & y are of same sign ∴ x + iy = +(5 + 4i) or = (5 + 4i)