Given :
(1+i)22−i=x+iy
L.H.S.=(1+i)22−i
⇒L.H.S.=1+i2+2i2−i
⇒L.H.S.=1−1+2i2−i {∵i2=−1}
→L.H.S.=2i2−i
Multiplying and dividing by
conjugate of denominator in L.H.S.
⇒L.H.S.=2i(2+i)(2−i)(2+i)=4i+2i24−i2=4i−24−(−1)
⇒L.H.S.=−2+4i5
⇒L.H.S.=−25+45i
Comparing L.H.S. and R.H.S.
∵L.H.S.=R.H.S.
∴−25+45i=x+iy
Comparing corresponding real and imaginary part
⇒x=−25,y=45
Hence, x+y=−25+45=25