`[(sqrt(5)+i/2)(sqrt(5)-i2)]-:(6+i5)`

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0

Simplify the following expressions. (i) (5+sqrt(7))(2+sqrt(5)) (ii) (5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(3)+sqrt(7))^2 (iv) (sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))

Find the following as a single complex number x+ iy (sqrt(6)+i5)(sqrt(6)-i(1)/(5))

If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5 , then prove that I m(z)=0.

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

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

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))

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))

Simplify :- (i) (6)/(sqrt(2)) (ii) (sqrt(3))/(3) (iii) sqrt((3)/(4)) (iv) (6)/(sqrt(2)) (v) (sqrt(5))/(10) (vi) sqrt((16)/(2))