Question

The reciprocal of the radicand of 3√7 is.....​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

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 )

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

3− √7 i