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Q.
What is the reciprocal of $3+\sqrt{7}\,i$ ?
Complex Numbers and Quadratic Equations
Solution:
Reciprocal of $z=\frac{\bar{z}}{\left|z\right|^{2}}$
Therefore, reciprocal of $3+\sqrt{7}i=\frac{3-\sqrt{7}i}{16}$
$=\frac{3}{16}-\frac{\sqrt{7}\,i}{16}$