((3+i sqrt(5))(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)))

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

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

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

Evaluate: (iv) ((3+sqrt5i)(3-sqrt5i))/((sqrt3+sqrt2i)-(sqrt3-sqrt2i))

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 (i) (3-sqrt(11))(3+sqrt(11)) (ii) (-3+ sqrt(5))(-3-sqrt(3)-sqrt(5)) (iii) (3- sqrt(3))^(2) (iv) (sqrt(5) - sqrt(3))^(2) (v) (5+ sqrt(7))(2+ sqrt(5)) (vi) (sqrt(5) - sqrt(2))(sqrt(2) - sqrt(3))

Simplify each of the following expressions: (i) (3+sqrt(3))(2+sqrt(2)) (ii) (3+sqrt(3))(3-sqrt(3)) (iii) (sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))