The number of complex numbersd z, such that `abs(z-1)=abs(z+1)=abs(z-i)`, where `i=sqrt(-1)` equals to

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

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

Consider the two complex numbers z and w, such that w=(z-1)/(z+2)=a+ib, " where " a,b in R " and " i=sqrt(-1). If z=CiStheta , which of the following does hold good?

For every real number c ge 0, find all complex numbers z which satisfy the equation abs(z)^(2)-2iz+2c(1+i)=0 , where i=sqrt(-1) and passing through (-1,4).

Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) Then ,|z| is equal to

bb"statement-1" " Let " z_(1),z_(2) " and " z_(3) be htree complex numbers, such that abs(3z_(1)+1)=abs(3z_(2)+1)=abs(3z_(3)+1) " and " 1+z_(1)+z_(2)+z_(3)=0, " then " z_(1),z_(2),z_(3) will represent vertices of an equilateral triangle on the complex plane. bb"statement-2" z_(1),z_(2),z_(3) represent vertices of an triangle, if z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)=0

If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

Let z be a complex number satisfying |z-5i|<=1 such that amp(z) is minimum, then z is equal to

If the complex number z is to satisfy abs(z)=3, abs(z-{a(1+i)-i}) le 3 and abs(z+2a-(a+1)i) gt 3 , where i=sqrt(-1) simultaneously for atleast one z, then find all a in R .

If z is any complex number satisfying abs(z-3-2i) le 2 , where i=sqrt(-1) , then the minimum value of abs(2z-6+5i) , is