(((3+2i))/((2-3i))+((3-2i))/((2+3i))}" is purely real,"

Show that the complex number ((4+3i)/(3 + 4i)) ((4 -3i)/(3-4i)) is purely real.

Show that the complex number ((4+3i)/(3 + 4i)) ((4 -3i)/(3-4i)) is purely real.

Prove that (sqrt(3)/(2) +(i)/(2))^(5) + (sqrt(3)/(2) -(i)/(2))^(5) is purely real.

Prove that: (i) [((3+2i)/(2-5i))+((3-2i)/(2+5i))] is rational (ii) [((2-3i)/(3-4i))((2+3i)/(3+4i))] is real.

Show that ((19+9i)/(5-3i))^(15)-((8+i)/(1+2i))^(15) is purely imaginary.

((2+3i)/(2-3i))-((2-3i)/(2+3i)) in the form of a + ib

Prove that : [((2-3i)/(3-4i))((2+3i)/(3+4i))] is real .

Show that (1+ 2i)/(3+4i) xx (1-2i)/(3-4i) is real