Let z=9+ai, where `i=sqrt(-1)` and a be non-zero real.
If `Im(z^(2))=Im(z^(3))`, sum of the digits of `a^(2)` is

If z(2-i)=3+I,z^(20) =

If |z^(2)-1|=|z|^(2)+1 , then z lies on :

Let z=(-1+sqrt(3)i)/(2) , where i=sqrt(-1) , and r, s in {1, 2, 3} . Let P=[((-z)^(r),z^(2s)),(z^(2s),z^(r))] and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P^(2)=-I is ______.

If z=(sqrt(3)-i)/2 , where i=sqrt(-1) , then (i^(101)+z^(101))^(103) equals to

If Im((z-1)/(2 z+1))=-4 then the locus of z is

If w=(z)/(z-(1)/(3)i) and |w|=1 , then z lies on

If |(z+i)/(z-i)|=sqrt(3) , then the radius of the circle is

If omega=(z)/(z-(i)(3)) and |omega|=1 , the z lies on

Let z=cos theta+isintheta . Then the value of sum_(m-1)^(15)Im(z^(2m)-1) at theta=2^(@) is

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is