Question

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

• A. $\frac{3}{16}-\frac{1}{16}i$
• B. $\frac{3}{16}+\frac{1}{16}i$
• C. $\frac{3}{16}+\frac{\sqrt{7}}{16}i$
• D. $\frac{3}{16}-\frac{\sqrt{7}}{16}i$

Answer 1

Answer: (D)

Reciprocal of $z=\frac{\bar{z}}{{|z|}^2}$
Therefore, reciprocal of $3+\sqrt{7}i=\frac{3-\sqrt{7}i}{16}$
$=\frac{3}{16}-\frac{\sqrt{7}i}{16}$