Let α be a root of the equation 1 + x2 + x4 = 0. Then the value of α1011 + α2022 – α3033 is equal to
Let α be a root of the equation 1 + x2 + x4 = 0. Then the value of α1011 + α2022 – α3033 is equal to
- 1
- α
- 1+α
- 1+2α
The Correct Option is A
Solution and Explanation
The correct answer is (A) : 1
1 + x2 + x4 = 0
ω1011 + ω2022 - ω3033
= (ω3)337 + (ω3)674 - (ω3)1011
= 1+1-1
= 1
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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.