Question:
What is the reciprocal of $3+\sqrt{7}\,i$ ?
What is the reciprocal of $3+\sqrt{7}\,i$ ?
Updated On: Jul 7, 2022
- $\frac{3}{16}-\frac{1}{16} i$
- $\frac{3}{16}+\frac{1}{16} i$
- $\frac{3}{16}+\frac{\sqrt{7}}{16} i$
- $\frac{3}{16}-\frac{\sqrt{7}}{16} i$
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The Correct Option is D
Solution and Explanation
Reciprocal of $z=\frac{\bar{z}}{\left|z\right|^{2}}$
Therefore, reciprocal of $3+\sqrt{7}i=\frac{3-\sqrt{7}i}{16}$
$=\frac{3}{16}-\frac{\sqrt{7}\,i}{16}$
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
