Simplify: `(5+sqrt(2)i)/(1-sqrt(2)i)`

Rationalies the denominator and simplify: (i) (1+sqrt(2))/(3-2sqrt(2)) (ii) (2sqrt(6)-\ sqrt(5))/(3sqrt(5)-\ 2sqrt(6))

Simplify: sqrt(3-2sqrt(2))

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

Express the following complex numbers in the standard form a+i b :(5+sqrt(2)i)/(1-sqrt(2)i)

Simplify: (sqrt(-2))/(sqrt(-8))

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

Simplify: (i) (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))

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

Simplify : sqrt(3+2sqrt(2))

Simplify : (i) (sqrt(5)+sqrt(2))^2 (ii) (sqrt(11)-sqrt(5))^2