Find the values of x and y which satisfy the following equations (x, y ∈ R) (x + 1)/(1 + i) + (y - 1)/(1 - i) = i

Question

Find the values of x and y which satisfy the following equations (x, y ∈ R)

\(\frac{x+1}{1+i}+\frac{y-1}{1-i}=i\)

(x + 1)/(1 + i) + (y - 1)/(1 - i) = i

Answer 1

\(\frac{x+1}{1+i}+\frac{y-1}{1-i}=i\) 

(x + y) + (y – x – 2)i = 2i

(x + y) + (y – x – 2)i = 0 + 2i

Equating real and imaginary parts, we get

x + y = 0 and y – x – 2 = 2

∴ x + y = 0 …….(i)

and -x + y = 4 …….(ii)

Adding (i) and (ii), we get

2y = 4

∴ y = 2

Substituting y = 2 in (i), we get

x + 2 = 0

∴ x = -2

∴ x = -2 and y = 2