Simplify `((sqrt(3)-i sqrt(2))(sqrt(2)+i sqrt(3)))/((sqrt(2)-i sqrt(3))(sqrt(2)+i sqrt(3)))`

(sqrt(3)-i sqrt(2))/(2sqrt(3)-i sqrt(2))

( (sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3)) )/( (sqrt(3)+i sqrt(2))+(sqrt(3)-i sqrt(2)) )

((sqrt(3)+i sqrt(5))(sqrt(3)-i sqrt(5)))/((sqrt(3)+sqrt(2)i)-(sqrt(3)-i sqrt(2))

Simplify ((sqrt(5)-sqrt(3))(sqrt(5)+sqrt(3)))/((sqrt(5)+2)+(2-sqrt(5)))

Simplify (sqrt(3)+sqrt(2))(sqrt(2)-sqrt(3))

([(sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

Simplify (sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))

Show that (i)" "{((3+2i))/((2-3i))+((3-2i))/((2+3i))} is purely real, (ii)" "{((sqrt(7)+i sqrt(3)))/((sqrt(7)-i sqrt(3)))+((sqrt(7)- i sqrt(3)))/((sqrt(7) + i sqrt(3)))} is purely real.

Simplify: (3sqrt(2)-2sqrt(2))/(3sqrt(2)+2sqrt(3))+(sqrt(12))/(sqrt(3)-sqrt(2)) (ii) (sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))