JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(\mathrm{z}\) is a complex number, then the number of common roots of the equation \(z^{1985}+z^{100}+1=0\) and \(z^3+2 z^2+2 z+1=0\), is equal to :
- A \(1\)
- B \(2\)
- C \(0\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(z^{1985}+z^{100}+1=0 \quad \& z^3+2 z^2+2 z+1=0 \) \((z+1)\left(z^2-z+1\right)+2 z(z+1)=0\) \((z+1)\left(z^2+z+1\right)=0\)…
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