The region represented by
{z = x + iy $$ \in $$ C : |z| – Re(z) $$ \le $$ 1} is also given by the
inequality : {z = x + iy $$ \in $$ C : |z| – Re(z) $$ \le $$ 1}

The area (in sq. units) of the region
A = {(x, y) : |x| + |y| $$ \le $$ 1, 2y² $$ \ge $$ |x|}

If $$\alpha $$ and $$\beta $$ be two roots of the equation
x² – 64x + 256 = 0. Then the value of
$${\left( {{{{\alpha ^3}} \over {{\beta ^5}}}} \right)^{1/8}} + {\left( {{{{\beta ^3}} \over {{\alpha ^5}}}} \right)^{1/8}}$$ is :

The values of $$\lambda $$ and $$\mu $$ for which the system of linear equations
x + y + z = 2
x + 2y + 3z = 5
x + 3y + $$\lambda $$z = $$\mu $$
has infinitely many solutions are, respectively: