The number of complex numbers z such that |z-1|=|z+1|=|z-i| equals

Step-by-step solution

Let z=x+i y array lll |z-1|=|z+1| & Re z=0 & x=0 |z-1|=|z-i| & x=y & |z+1|=|z-i| & y=-x & array Only (0,0) will satisfy all conditions. Number of complex number z=1