Question

reciprocal of 3+i√7​

Answer 1

Answer:

Given complex number,

3 + √7i,

Since, the reciprocal of a complex number z is \frac{1}{z}z1

Thus, the reciprocal of the given number,

\frac{1}{3+\sqrt{7}i}3+7i1

For rationalizing the denominator, multiply both numerator and denominator by 3 - √7i,

We get,

\frac{3-\sqrt{7}i}{9-7i^2}9−7i23−7i

\frac{3-\sqrt{7}i}{9+7}9+73−7i ( i² = -1 )

\frac{3-\sqrt{7}i}{16}163−7i