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4-1.Complex numbers
medium
$\frac{{\sqrt {5 + 12i} + \sqrt {5 - 12i} }}{{\sqrt {5 + 12i} - \sqrt {5 - 12i} }} = $
A
$ - \frac{3}{2}i$
B
$\frac{3}{2}i$
C
$ - \frac{3}{2}$
D
$\frac{3}{2}$
Solution
(a)$\frac{{(\sqrt {5 + 12i} + \sqrt {5 – 12i} )(\sqrt {5 + 12i} + \sqrt {5 – 12i} )}}{{(\sqrt {5 + 12i} – \sqrt {5 – 12i} )(\sqrt {5 + 12i} + \sqrt {5 – 12i} )}}$
$ = \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 $\frac{{2i}}{3}$.
Standard 11
Mathematics
