Experts!! Please answer!! How can we find the real values of x y, if : (x -1 - Maths - Complex Numbers and Quadratic Equations

Question

Experts!! Please answer!! How can we find the real values of x
& y, if : (x -1 / 3 + i) + (y - 1 / 3 - i) = i????

Ankush Jain · Accepted Answer

Given,

$\frac{x - 1}{3 + i} + \frac{y - 1}{3 - i} = i \Rightarrow \frac{(x - 1) (3 - i) + (y - 1) (3 + i)}{(3 + i) (3 - i)} = i \Rightarrow \frac{3 x - 3 - i x + i + 3 y - 3 + i y - i}{9 - i^{2}} = i \Rightarrow \frac{3 x + 3 y - 6 - i x + i y}{9 - (- 1)} = i \Rightarrow \frac{3 x + 3 y - 6}{10} + \frac{(- i x + i y)}{10} = i \Rightarrow \frac{3 x + 3 y - 6}{10} + \frac{i (- x + y)}{10} = 0 + 1 i$

Now, on comparing real and imaginary parts, we get

$\frac{3 x + 3 y - 6}{10} = 0 and \frac{(- x + y)}{10} = 1 \Rightarrow 3 x + 3 y = 6 and - x + y = 10 \Rightarrow x + y = 2 and - x + y = 10$

On adding, we get

$2 y = 12 \Rightarrow y = 6 \Rightarrow x + 6 = 2 \Rightarrow x = - 4$

Experts!! Please answer!!. How can we find the real values of x & y, if : (x -1 / 3 + i) + (y - 1 / 3 - i) = i????