Question:
Find the value of $\frac{i^{4n+1}-i^{4n-1}}{2}$ .
Find the value of $\frac{i^{4n+1}-i^{4n-1}}{2}$ .
Updated On: Jul 6, 2022
- $i$
- $2i$
- $-i$
- $-2i$
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The Correct Option is A
Solution and Explanation
$\frac{i^{4n+1}-i^{4n-1}}{2}$
$=\frac{i^{4n} i-i^{4n}i^{-1}}{2}$
$=\frac{i^{2}-1}{2i}$
$=\frac{-2}{2i}$
$=i$
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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.
