Question

If z = x + iy, z^1/3 = a – ib, a ¹ ±ba, b ¹ 0 then $\frac{x}{a} - \frac{y}{b}$ = k(a² – b²), where k = _______

• A. 4
• B. 3
• C. 2
• D. None

Answer 1

Answer: (A)

4

Answer 2

Sol. We have (x + iy)^1/3 = a – ib

Ž x + iy = (a – ib)³ = (a³ – 3ab²) + i(b³ – 3a²b)

Ž x = a³ – 3ab² and y = b³ – 3a²b

Ž $\frac{x}{a}$ = a² – 3b² and $\frac{y}{b}$ = b² – 3a²

Ž $\frac{x}{a}$ – $\frac{y}{b}$ = 4 (a² – b²) = 4(a² – b²)

Thus k = 4.