Question

Find the square of $\sqrt{9+40\sqrt{-1}}+\sqrt{9-40\sqrt{-1}}$

Answer 1

${(\sqrt{9+40\sqrt{-1}}+\sqrt{9-40\sqrt{-1}})}^2$

$={(\sqrt{9+40\text{i}}+\sqrt{9-40\text{i}})}^2$

$=9+40\text{i}+9-40\text{i}+2\sqrt{9+40}$

$=32$