Question

find the reciprocal of 3+root7i​

Answer 1

Answer:

Answer:

\frac{3-\sqrt{7}i}{16}

16

3−

7

i

Step-by-step explanation

Given complex number,

3 + √7i,

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

z

1

Thus, the reciprocal of the given number,

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

3+

7

i

1

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

We get,

\frac{3-\sqrt{7}i}{9-7i^2}

9−7i

2

3−

7

i

\frac{3-\sqrt{7}i}{9+7}

9+7

3−

7

i

( i² = -1 )