Let z be a complex number such that |z| + z = 3 + i (where i = $$\sqrt { - 1} $$). Then |z| is equal to :

Let $${\left( { - 2 - {1 \over 3}i} \right)^3} = {{x + iy} \over {27}}\left( {i = \sqrt { - 1} } \right),\,\,$$ where x and y are real numbers, then y $$-$$ x equals :

Let $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5}.$$ If R(z) and 1(z) respectively denote the real and imaginary parts of z, then :

Let z₁ and z₂ be any two non-zero complex numbers such that   $$3\left| {{z_1}} \right| = 4\left| {{z_2}} \right|.$$  If  $$z = {{3{z_1}} \over {2{z_2}}} + {{2{z_2}} \over {3{z_1}}}$$  then :