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 and y=2

Step-by-step explanation:

(x+1) \ (1+i ) + ( y-1) \ (1-i )  = i​

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

=(x+1-xi-i) /(1-i²) + (y-1+yi-i) /(1-i²)

=1/2 ( x+1-xi-i+y-1+yi-i)

=1/2( x+y-i(x-y+2) )

Or (x+y)/2 -i(x-y+2)/2=RHS=i= 0+i

on comparision we get

x+y/2=0 or x+y=0

so y=-x

and -(x-y+2)2=1

x-y+2=-2

x+x=-4

x=-2

and y=-(-2)=2