Question:
Express $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$ in the form of $a + ib$ .
Express $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$ in the form of $a + ib$ .
Updated On: Jul 6, 2022
- $1-2 \sqrt{2}i$
- $1-\sqrt{2}i$
- $1+2\sqrt{2}i$
- $1+\sqrt{2}i$
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The Correct Option is C
Solution and Explanation
We have, $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$
$=\frac{5+\sqrt{2}i}{1-\sqrt{2}i}\times\frac{1+\sqrt{2}i}{1+\sqrt{2}i}$
$=\frac{5+5\sqrt{2}i+\sqrt{2}i-2}{1-\left(\sqrt{2}i\right)^{2}}$
$=\frac{3\left(1+2 \sqrt{2}i\right)}{3}$
$=1+2\sqrt{2}i$
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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.
