Solveeit Logo
Login

Question

Mathematics Question on Complex Numbers and Quadratic Equations

What is the reciprocal of 3+7 i3+\sqrt{7}\,i ?

A

316−116i\frac{3}{16}-\frac{1}{16} i

B

316+116i\frac{3}{16}+\frac{1}{16} i

C

316+716i\frac{3}{16}+\frac{\sqrt{7}}{16} i

D

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

Answer

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

Explanation

Solution

Reciprocal of z=zˉ∣z∣2z=\frac{\bar{z}}{\left|z\right|^{2}} Therefore, reciprocal of 3+7i=3−7i163+\sqrt{7}i=\frac{3-\sqrt{7}i}{16} =316−7 i16=\frac{3}{16}-\frac{\sqrt{7}\,i}{16}