Question

The real values of x and y for which the equation

$(x^{4} + 2xi) - (3x^{2} + yi) = (3 - 5i) + (1 + 2yi)$ is satisfied, are

• A. $x = 2,y = 3$
• B. $x = - 2,y = \frac{1}{3}$
• C. Both (1) and (2)
• D. None of these

Answer 1

Answer: (C)

Both (1) and (2)

Answer 2

Sol. Given equation $(x^{4} + 2xi) - (3x^{2} + yi) = (3 - 5i) + (1 + 2yi)$

⇒ $(x^{4} - 3x^{2}) + i(2x - 3y) = 4 - 5i$

Equating real and imaginary parts, we get

$x^{4} - 3x^{2} = 4$ .....(i) and $2x - 3y = - 5$ .....(ii)

Form (i) and (ii), we get $x = \pm 2$ and $y = 3,\frac{1}{3}.$

Trick: Put $x = 2,y = 3$ and then $x = - 2,y = \frac{1}{3},$ we see that they both satisfy the given equation.