TS EAMCET · Maths · Complex Number
The number of complex roots of the equation \(x^{11}-x^7+x^4-1=0\) whose arguments lie in the first quadrant is
- A 2
- B 3
- C 7
- D 9
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { } x^{11}-x^7+x^4-1=0 \\ & x^7\left(x^4-1\right)+1\left(x^4-1\right)=0 \\ & \quad\left(x^7+1\right)\left(x^4-1\right)=0 \\ & (x+1)\left(x^6-x^5+x^4-x^3+x^2-x+1\right)\left(x^2+1\right) \\ & \qquad\left(x^2-1\right)=0 \end{aligned} \] So, number of…
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