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.
