When 'a' is real number then `(z+a)(bar(z)+a)=`________.

If (7+i)(z + bar(z))-(4+i)(z-bar(z)) + 116i = 0 then z bar(z) is equal to ______________.

If z is a nonzero complex number then (bar(z^-1))=(barz)^-1 .

The number of solutions of z^(2)+bar(z)=0 is

The number of solutions of z^(2)+bar(z)=0 is

If z is a complex number such taht z^(2)=(bar(z))^(2) then find the location of z on the Argand plane.

Let z=1+ ai be a complex number,a>0, such that z^(3) is a real number.Then the sum 1+z+z^(2)+...+z^(11) is equal to:

Let z=log_(2)(1+i) then (z+bar(z))+i(z-bar(z))=