Question

if (a+ib)^2=x+iy find x^2+y^2​

Answer 1

(a+ib)² = x+iy

=> a² + (ib)² + 2(a)(ib) = x + iy

=> a² - b² + i2ab = x + iy

{ Comparing both sides }

=> x = a² - b² and y = 2ab

now , x² + y² = ( a² - b²)² + ( 2ab)²

=> a⁴ + b⁴ - 2a²b² + 4a²b²

=> a⁴ + b⁴ + 2a²b²

=> (a²)² + (b²)² + 2(a²)(b²)

=> ( a² + b² )²...... is the answer