Show that [`frac{sqrt 7+i sqrt 3}{sqrt 7-i sqrt 3}`+`frac{sqrt 7-i sqrt 3}{sqrt 7+i sqrt 3}`is real.

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

Simplify 7 sqrt 3-29 sqrt 3

Show that (frac{1}{sqrt 2}+frac{1}{sqrt 2}i )^10 + (frac{1}{sqrt 2}-frac{1}{sqrt 2}i )^10 = 0

Show that (sqrt(3)/2 + i/2)^3 = i

If (5 sqrt 2+3 sqrt 3)-(6 sqrt 2-7 sqrt 3)=a sqrt 2+b sqrt 3 then find a and b.

The amplitude of frac{1+sqrt3i}{sqrt3+i} is

Multiply: \sqrt{3} (\sqrt{7} -\sqrt{3})

Show that (frac{1+i}{sqrt 2})^8 + (frac{1-i}{sqrt 2})^8 = 2

Express the following expression in the form (a+ib), frac{(3+i sqrt 5)(3-i sqrt 5)}{(sqrt 3 + sqrt 2 i) - (sqrt 3 - sqrt 2 i)}