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^(4)+1=0,"where"i=sqrt(-1) then z can take the value

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

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(2)/(z))=4 and sum of greatest and least values of abs(z) is lambda , then lambda^(2) , is

If z=(1+i)/(√2) , then the value of z^(1929) is

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

If z^(3)+(3+2i)z+(-1+ia)=0, " where " i=sqrt(-1) , has one real root, the value of a lies in the interval (a in R)

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(3)/(z))=6 and sum of greatest and least values of abs(z) is 2lambda , then lambda^(2) , is

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(1)/(z))=2 and sum of greatest and least values of abs(z) is lambda , then lambda^(2) , is

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Im (z) equals to

Let P point denoting a complex number z on the complex plane. i.e. z=Re(z)+i Im(z)," where "i=sqrt(-1) if" "Re(z)=x and Im(z)=y,then z=x+iy .The area of the circle inscribed in the region denoted by |Re(z)|+|Im(z)|=10 equal to