If `z` is a complex number and `z=bar(z)`, then prove that `z` is a purely real number.

If z is a complex number such that z=-bar(z) then

If z is a complex number, then (bar(z^-1))(bar(z)) =

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

Let z be a complex number such that |(z-5i)/(z+5i)|=1 , then show that z is purely real

If z is a complex number such that |z|=1, prove that (z-1)/(z+1) is purely imaginary, what will by your conclusion if z=1?

If z is a complex number such that |z|=1, prove that (z-1)/(z+1) is purely imaginary, what will be your conclusion if z=1?

If z is a complex number such that |z|=1, prove that (z-1)/(z+1) is purely imaginary, what will by your conclusion if z=1?

If |(z)/(|bar(z)|)-bar(z)|=1+|z|, then prove that z is a purely imaginary number.