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

Prove that z=i^i, where i=sqrt-1, is purely real.

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

If z=(3+4i)^(6)+(3-4i)^(6),"where" i=sqrt(-1), then Find the value of Im(z) .

Consider four complex numbers z_(1)=2+2i, , z_(2)=2-2i,z_(3)=-2-2iandz_(4)=-2+2i),where i=sqrt(-1), Statement - 1 z_(1),z_(2),z_(3)andz_(4) constitute the vertices of a square on the complex plane because Statement - 2 The non-zero complex numbers z,barz, -z,-barz always constitute the vertices of a square.

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

if Im((z+2i)/(z+2))= 0 then z lies on the curve :

If "Im"(2z+1)/(iz+1)=-2 , then locus of z, is

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

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

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)=xand Im (z)=y,then z=x+iy Number of integral solutions satisfying the eniquality |Re(z)|+|Im(z)|lt21,.is