Number of solutions of |z−1|+|z+i|=4 and |2z−1+i|=14 is

|z−1|+|z−i|=4 represents ellipse with foci (1,0) and (0,−1) and length of major axis =4 Centre of ellipse is 12,−12 and 1−i22a=4,2ae=2⇒e=122 From b2=a21−e2, we get b=72 Now |2z−1+i|=14⇒z−12+i2=72⇒z−1−i2=72 represents a circle having centre at 1−i2 and radius =72. Since radius of circle = minor axis of ellipse,Hence number of solution of given equation= 2.