The value of $\left(1-\omega+\omega^{2}\right)^{5} + \left(1+\omega -\omega^{2}\right)^{5}, $ where $\omega$ and $\omega^2$ are the complex cube roots of unity, is
- $0$
- $32 \,\omega$
- $-32$
- $32$
The Correct Option is D
Solution and Explanation
Top Questions on Complex numbers
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Questions Asked in WBJEE exam
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A quantity \( X \) is given by: \[ X = \frac{\epsilon_0 L \Delta V}{\Delta t} \] where:
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- \( \Delta V \) is the potential difference,
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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.