Question

answer to this ques. solved​

Answer 1

Answer :

Given, (x + iy)³ = u + iv

or, x³ + 3 x² (iy) + 3 x (iy)² + (iy)³ = u + iv

or, x³ + i3x²y - 3xy² - iy³ = u + iv,

since i² = - 1 and i³ = - i

or, (x³ - 3xy²) + (3x²y - y³)i = u + iv

Comparing among coefficients, we get

u = x³ - 3xy² and v = 3x²y - y³

∴ L.H.S. = u/x + v/y

= (x³ - 3xy²)/x + (3x²y - y³)/y

= x² - 3y² + 3x² - y²

= 4x² - 4y²

= 4 (x² - y²) = R.H.S.

Hence, proved.