Question:
Express $i^{-35}$ in the form of $a + ib$.
Express $i^{-35}$ in the form of $a + ib$.
Updated On: Jul 6, 2022
- $i$
- $-i$
- $1$
- $-2$
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The Correct Option is A
Solution and Explanation
$i^{-35}=\frac{1}{i^{35}}=\frac{1}{\left(i^{2}\right)^{17} i}$
$=\frac{1}{-i}\times\frac{i}{i}=\frac{i}{-i^{2}}$
$=i$
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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.
