Question

tf x+iy=a+ib/C+id,prove that x^2+y^2=a^2+b^2/c^2+d^2​

Answer 1

We can observe first that x²+y² is x+iy multiplied by its complex conjugate.

Both sides of x+iy and a+ib/c+id is equal. Their complex conjugate is also equal to each other:

→(x+iy)(x-iy) = (a+ib)/(c+id) * (a-ib)/(c-id)

→x²+y² = (a²+b²)/(c²+d²)

Always think outside the box