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Question

Question: The reciprocal of \(3 + \sqrt{7}i\) is...

The reciprocal of 3+7i3 + \sqrt{7}i is

A

34−74i\frac{3}{4} - \frac{\sqrt{7}}{4}i

B

3−7i3 - \sqrt{7}i

C

316−716i\frac{3}{16} - \frac{\sqrt{7}}{16}i

D

7+3i\sqrt{7} + 3i

Answer

316−716i\frac{3}{16} - \frac{\sqrt{7}}{16}i

Explanation

Solution

Sol.13+7i=13+7i.3−7i3−7i=3−7i9+7=3−7i16=316−716i.\frac{1}{3 + \sqrt{7}i} = \frac{1}{3 + \sqrt{7}i}.\frac{3 - \sqrt{7}i}{3 - \sqrt{7}i} = \frac{3 - \sqrt{7}i}{9 + 7} = \frac{3 - \sqrt{7}i}{16} = \frac{3}{16} - \frac{\sqrt{7}}{16}i.