Question 16:

Answer

(x + iy)³ = u + iv

⇒ x³ + (iy)³ + 3 ∙ x ∙ iy(x + iy) = u + iv

⇒ x³ + i³y³ + 3x²yi + 3xy²i² = u + iv

⇒ x³ – iy³ + 3x²­yi− 3xy² = u + iv

⇒ (x³ – 3xy²) + i(3x²y – y³) = u + iv

On equating real and imaginary parts, we obtain

u = x³ – 3xy², v = 3x²y – y³

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