NCERT Solution Class XI Mathematics Complex Numbers and Quadratic Equations Question 16 (Mis Ex)

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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