Q. 64.0( 4 Votes )

# Find real values of x and y for which

(x^{4} + 2xi) – (3x^{2} + iy) = (3 – 5i) + (1 + 2iy).

Answer :

We have, (x^{4} + 2xi) – (3x^{2} + iy) = (3 – 5i) + (1 + 2iy).

⇒ x^{4} + 2xi - 3x^{2} + iy = 3 – 5i + 1 + 2iy

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

On equating real and imaginary parts, we get

x^{4} - 3x^{2 =} 4 and 2x - y = 2y - 5

⇒ x^{4} - 3x^{2} - 4 = 0 eq(i) and 2x - y - 2y + 5 = 0 eq(ii)

Now from eq (i), x^{4} - 3x^{2} - 4 = 0

⇒ x^{4} - 4x^{2 +} x^{2} - 4 = 0

⇒ x^{2} (x^{2} - 4) ^{+} 1(x^{2} - 4) = 0

⇒ (x^{2} - 4)(x^{2} + 1) = 0

⇒ x^{2} - 4 = 0 and x^{2} + 1 = 0

⇒ x = ±2 and x = √ - 1

Real value of x = ±2

Putting x = 2 in eq (ii), we get

2x - 3y + 5 = 0

⇒ 2×2 - 3y + 5 = 0

⇒ 4 - 3y + 5 = 0 = 9 - 3y = 0

⇒ y = 3

Putting x = - 2 in eq (ii), we get

2x - 3y + 5 = 0

⇒ 2× - 2 - 3y + 5 = 0

⇒ - 4 - 3y + 5 = 0 = 1 - 3y = 0

⇒

Rate this question :

Evaluate.

RS Aggarwal - MathematicsEvaluate

RS Aggarwal - Mathematics

If (x + iy)^{1/3} = (a + ib) then prove that = 4 (a^{2} – b^{2}).

If then show that

RD Sharma - MathematicsProve that i^{53} + i^{72} + i^{93} + i^{102} = 2i.