Let z be a complex number such that z-iz+2i=1 and |z|=52, Then the value of z+3i is:

Given |z-i|2=|z+2i|2    ⇒x2+(y-1)2=x2+(y+2)2⇒-2y+1=4y+4⇒y=-12 Given |z|=52    It gives      x2+y2=254x2=244=6x=±6 It gives z=±6-i2 The required value is |z+3i|=6+5i2=6+254=∣72