Question

find the value of x and y which satisfy the following equation (x, y€R) 2) x+1\1+i + y-1\1-i=i​

Answer 1

Answer :

x = -2 , y = 2

Solution :

We have ,

(x + 1)/(1 + i) + (y - 1)/(1 - i) = i where x,y € R .

Now ,

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

=> [(x + 1)(1 - i) + (y - 1)(1 + i)] / (1 + i)(1 - i) = i

=> [x - ix + 1 - i + y + iy - 1 - i] / [1² - i²] = i

=> [x + y - ix + iy - 2i] / [1 - (-1)] = i

=> [(x + y) + (-x + y - 2)i] / [1 + 1] = i

=> [(x + y) + (-x + y - 2)i] / 2 = i

=> [(x + y) + (-x + y - 2)i] = 2i

=> (x + y) + (-x + y - 2)i = 0 + 2i

Now ,

Comparing both the sides , we have ;

x + y = 0 ------(1)

-x + y - 2 = 2 → -x + y = 4 ------(2)

Now ,

Adding eq-(1) and (2) , we get ;

=> x + y - x + y = 0 + 4

=> 2y = 4

=> y = 4/2

=> y = 2

Now ,

Putting y = 2 in eq-(1) , we get ;

=> x + y = 0

=> x + 2 = 0

=> x = -2

Hence ,

x = -2 , y = 2