Let u=2z+iz-ki,z=x+iy and k>0. If the curve represented by Re(u)+Im(u)=1 intersects the y - axis at the points P and Q where PQ = 5, then the value of k is :

u=2z+iz-ki=2(x+iy)+ix+iy-ki=2x+i(2y+1)x+i(y-k)×x-i(y-k)x-i(y-k)Reu=2x2+(2y+1)(y-k)x2+(y-k)2 Img u=x(2y+1)-2x(y-k)x2+(y-k)2 Reu + Img u=1  y -axis ⇒put x=0  in (1) (2y+1)(y-k)(y-k)2=1y−ky+1+k=0y=k,−1+kP(0,k),Q(0,-1-k) and PQ=5⇒2 K+1=5, -2k-1=52 K=4,-6⇒K=2,-3;K>0⇒K=2