Find the multiplicative inverse of the complex numbers = 5 + 3i - Vidyadip

Question

Find the multiplicative inverse of the complex numbers $ = \sqrt 5 + 3i$

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Answer

M.I. of $ = \sqrt 5 + 3i$
$ = \frac{1}{{\sqrt 5 + 3i}} = \frac{1}{{\sqrt 5 + 3i}} \times \frac{{\sqrt 5 - 3i}}{{\sqrt 5 - 3i}}$
$ = \frac{{\sqrt 5 - 3i}}{{{{(\sqrt 5 )}^2} - {{(3i)}^2}}}$
$ = \frac{{\sqrt 5 - 3i}}{{5 - 9{i^2}}} = \frac{{\sqrt 5 - 3i}}{{5 + 9}} = \frac{1}{{14}}(\sqrt 5 - 3i)$

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