`(sqrt(3)+i sqrt(2))(sqrt(2)+i sqrt(3))=`..........

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

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

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

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

sqrt(i)-sqrt(-i)=sqrt(2)

sqrt(i)+sqrt(-i)=sqrt(2)

Express in the form a+ib : (sqrt(3)-i sqrt(2))/(2sqrt(3)-i sqrt(3))

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.

( (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))])