If (1+i) x-i 2+i + (1+2 i) y+i 2-i =1 , then (x, y) is equal to

Step-by-step solution

aligned & (1+i) x-i 2+i + (1+2 i) y+i 2-i =1 & [(1+i) x-i](2-i) (4-i^2 ) + [(1+2 i) y+i](2+i) (4-i^2 ) =1 & 2(1+i) x-2 i-i(1+i) x+i^2 4+1 & + 2(1+2 i) y+2 i+i(1+2 i) y+i^2 (4+1) =1 & (2+2 i-i-i^2 ) x-2 i+i^2 5 & + (4 i+2+i+2 i^2 ) y+2 i+i^2 5 =1 & (2+i+1) x-2 i-1 5 + (5 i+2-2) y+2 i-1 5 =1 & (3+i) x-2 i-1+(5 i) y+2 i-1=5 & (3+i) x+5 i y=7 & 3 x+i x+5 i y-7=0 & (3 x-7)+(x+5 y) i=0+i 0 & aligned On comparing, we get gathered 3 x-7=0 x= 7 3 and x+5 y=0 y= -7 15 gathered Hence, (x, y)= ( 7 3 , -7 15 )