A) \[-\frac{3}{2}i\]
B) \[\frac{3}{2}i\]
C) \[-\frac{3}{2}\]
D) \[\frac{3}{2}\]
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 \[\frac{2i}{3}\].
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