(sqrt(7)+sqrt(3)i)/(sqrt(7)-sqrt(3)i)+(sqrt(7)-sqrt(3)i)/(sqrt(7)+sqrt(3)i)

(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3))-(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3))

given x=(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3)),y=(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3)) find the value of x^(4)+y^(4)+(x+y)^(4)

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

sqrt(3)(sqrt(7)-sqrt(3))

1/(sqrt(7)+sqrt(3))\times (sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

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.

Show that (sqrt(7) + isqrt(3)) / (sqrt(7) - isqrt(3)) + (sqrt(7) - isqrt(3)) / (sqrt(7) + isqrt(3)) , is real.

(sqrt(7)-sqrt(5))^3 - (sqrt(7)+sqrt(5))^3