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Question:
The value of $ (1 + \omega - \omega^2)^7$ is
The value of $ (1 + \omega - \omega^2)^7$ is
Updated On: Apr 19, 2024
- $128 \, \omega^2$
- $ - 128 \, \omega^2$
- $128 \, \omega$
- $ - 128 \, \omega$
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The Correct Option is B
Solution and Explanation
$(1 + \omega - \omega^2)^7 = (- \omega^2 - \omega^2)^7 = (-2 \omega^2)^7$
$= -128 ( \omega^4)^3 \omega^2 = - 128 \, \omega^2$
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Concepts Used:
Complex Number
A Complex Number is written in the form
a + ib
where,
- “a” is a real number
- “b” is an imaginary number
The Complex Number consists of a symbol “i” which satisfies the condition i^2 = −1. Complex Numbers are mentioned as the extension of one-dimensional number lines. In a complex plane, a Complex Number indicated as a + bi is usually represented in the form of the point (a, b). We have to pay attention that a Complex Number with absolutely no real part, such as – i, -5i, etc, is called purely imaginary. Also, a Complex Number with perfectly no imaginary part is known as a real number.
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