If (x + iy)1/3 = a + ib, then \(\frac{x}{a}+\frac{y}{b}\) =A. 0 B.

1.	If (x + iy)1/3 = a + ib, then \(\frac{x}{a}+\frac{y}{b}\) =A. 0 B. 1 C. -1 D. None of these
Answer» x + iy)^1/3= a + ib x + iy = (a + ib)³ = a³ + (ib)³ + 3a²(ib) + 3a(ib)² = a³ – ib³ + i3a²b – 3ab² = (a³– 3ab²) + i(3a²b – b3) x = a³– 3ab² and y = 3a²b – b³ \(\frac{x}{a}+\frac{y}{b}\) = \(\frac{a^3-3ab^2}{a}+\frac{3a^2b-b^3}{b}\) = a³– 3b² + 3a² – b³ = 4(a² – b²)

If (x + iy)1/3 = a + ib, then \(\frac{x}{a}+\frac{y}{b}\) =A. 0 B. 1 C. -1 D. None of these

Answer»

x + iy)^1/3= a + ib

x + iy = (a + ib)³

= a³ + (ib)³ + 3a²(ib) + 3a(ib)²

= a³ – ib³ + i3a²b – 3ab²

= (a³– 3ab²) + i(3a²b – b3)

x = a³– 3ab² and y = 3a²b – b³

\(\frac{x}{a}+\frac{y}{b}\) = \(\frac{a^3-3ab^2}{a}+\frac{3a^2b-b^3}{b}\)

= a³– 3b² + 3a² – b³

= 4(a² – b²)