Find the real numbers x and y if (x - iy)(3 + 5i) is the conjugate of

1.	Find the real numbers x and y if (x - iy)(3 + 5i) is the conjugate of -6 - 24i.1. 3, 32. -3, 33. 3, -34. None of these.
Answer» Correct Answer - Option 3 : 3, -3 Concept: The conjugate of the complex number a + bi is a - bi. Property of iota power: i² = -1 i⁴ = 1 Calculation: Given: (x - iy)(3 + 5i) is the conjugate of -6 - 24i According to the question, (x - iy)(3 + 5i) = -6 + 24i. ⇒ 3x + 5xi - 3yi - 5yi² = -6 + 24i ⇒ (3x + 5y) + (5x - 3y)i = -6 + 24i Comparing the real and imaginary parts, we get: 3x + 5y = -6 ...(1) 5x - 3y = 24 ...(2) Multiplying equation (1) by 3 and equation (2) by 5 and adding, we get: 9x + 25x = -18 + 120 34x = 102 x = 3 Using equation (1), we get: y = -3.

Find the real numbers x and y if (x - iy)(3 + 5i) is the conjugate of -6 - 24i.1. 3, 32. -3, 33. 3, -34. None of these.

Answer» Correct Answer - Option 3 : 3, -3

Concept:

The conjugate of the complex number a + bi is a - bi.

Property of iota power:

i² = -1

i⁴ = 1

Calculation:

Given: (x - iy)(3 + 5i) is the conjugate of -6 - 24i

According to the question, (x - iy)(3 + 5i) = -6 + 24i.

⇒ 3x + 5xi - 3yi - 5yi² = -6 + 24i

⇒ (3x + 5y) + (5x - 3y)i = -6 + 24i

Comparing the real and imaginary parts, we get:

3x + 5y = -6 ...(1)

5x - 3y = 24 ...(2)

Multiplying equation (1) by 3 and equation (2) by 5 and adding, we get:

9x + 25x = -18 + 120

34x = 102

x = 3

Using equation (1), we get:

y = -3.

Discussion

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