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

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

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

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

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

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

(-sqrt3 + sqrt(-2))(2sqrt3-i)

(-sqrt3 + sqrt(-2))(2sqrt3 - i)

Simplify the following expressions: (i) (4+sqrt(7))(3+sqrt(2)) (ii) (3+sqrt(3))(5-sqrt(2)) (iii) (sqrt(5)-2)(sqrt(3)-sqrt(5)) (iv) (sqrt(5)+sqrt(2))(sqrt(3)+sqrt(2))

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