Simplify :
`(( 3 + iota sqrt(5) )( 3 - iota sqrt(5) ))/( ( 3 + sqrt(2) iota )- ( 3 - iota sqrt(2) ))`

sqrt(5+12 iota)

Simplify : ((2 sqrt(45) + 3 sqrt(20)))/(2sqrt5)

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

Simplify: a.(4 iota^(3)-iota)/(2 iota+1) b.(sqrt(3)+iota)^(6)

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

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

Simplify: (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

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))