# What is the reciprocal of $\;3+ \sqrt{7} i$

$(a)\;\large\frac{11}{16} - \large\frac{\sqrt{7}}{16} i\qquad(b)\;\large\frac{3}{16} - \large\frac{\sqrt{7}}{16} i\qquad(c)\;\large\frac{7}{16} - \large\frac{\sqrt{5}}{16} i\qquad(d)\;\large\frac{3}{16} - \large\frac{\sqrt{5}}{16} i$

Answer : $\;\large\frac{3}{16} - \large\frac{\sqrt{7}}{16} i$
Explanation :
Reciprocal of $\;z = \large\frac{\overline{z}}{|z|^{2}}$
Therefore , The reciprocal of $\;3+ \sqrt{7} i$
$= \large\frac{3-\sqrt{7} i}{16} = \large\frac{3}{16} - \large\frac{\sqrt{7}}{16}i \;.$