Complex Numbers And Quadratic Equations question 414
Question: $ \frac{\sqrt{5+12i}+\sqrt{5-12i}}{\sqrt{5+12i}-\sqrt{5-12i}}= $
Options:
A) $ -\frac{3}{2}i $
B) $ \frac{3}{2}i $
C) $ -\frac{3}{2} $
D) $ \frac{3}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{(\sqrt{5+12i}+\sqrt{5-12i})(\sqrt{5+12i}+\sqrt{5-12i})}{(\sqrt{5+12i}-\sqrt{5-12i})(\sqrt{5+12i}+\sqrt{5-12i})} $ $ =\frac{5+12i+5-12i+2\sqrt{5+12i}\sqrt{5-12i}}{5+12i-5+12i} $ $ =\frac{10+2\times (\pm 13)}{24i}=-\frac{3}{2}i $ or $ \frac{2i}{3} $ .
BETA
