Question

what is the reciprocal of 3 + √7i

Answer 1

Answer:

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

Step-by-step explanation:

Given complex number,

3 + √7i,

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

Thus, the reciprocal of the given number,

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

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

We get,

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

$\frac{3-\sqrt{7}i}{9+7}$ ( i² = -1 )

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

Answer 2

Answer:

−

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 )

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

16

3−

7

i