AP EAMCET · Maths · Complex Number
If \(\omega\) is a complex cube root of unity, then \((x+1)(x+\omega)(x-\omega-1)\) is equal to
- A \(x^3-1\)
- B \(x^3+1\)
- C \(x^3+2\)
- D \(x^3-2\)
Answer & Solution
Correct Answer
(A) \(x^3-1\)
Step-by-step Solution
Detailed explanation
\(\omega \rightarrow\) cube root of unity ie, \(\quad \omega^3=1\) and \(1+\omega+\omega^2=0\) Then, \((x+1)(x+\omega)(x-\omega-1)\) \(=(x+1)\left(x^2+\omega x-\omega x-\omega^2-x-\omega\right)\) \(=(x+1)\left(x^2-x-\left(\omega+\omega^2\right)\right)\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(A=(\alpha, 1,2 \alpha), B=(3,1,2)\) and \(\mathbf{C}=4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\). If \(\mathbf{A B} \times \mathbf{C}=6 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\), then \(\alpha^2+\alpha+5=\)AP EAMCET 2019 Easy
- The set of solutions satisfying both \(x^2+5 x+6 \geq 0\) and \(x^2+3 x-4 < 0\) isAP EAMCET 2013 Medium
- If a parabola passess through the points \((-2,1)\), \((1,2)\) and \((-1,3)\) having horizontal axis, then the length of the latus rectum of that parabola isAP EAMCET 2018 Medium
- The number of non-negative integral solutions of \(\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\mathrm{x}_4=10\) isAP EAMCET 2023 Easy
- The horizontal distance between a tower and a builidng is \(10 \sqrt{3}\) units. If the angle of depression of the foot of the building from the top of the tower is \(60^{\circ}\) and the angle of elevation of the top of the building from the foot of the tower is \(30^{\circ}\), then the sum of the heights of the tower and the building isAP EAMCET 2025 Medium
- If \(a x^4+b x^3+c x^2+50 x+d=\left|\begin{array}{ccc}x^3-14 x^2 & -x & 3 x+\lambda \\ 4 x+1 & 3 x & x-4 \\ -3 & 4 & 0\end{array}\right|\), then find ' \(\lambda\) '.AP EAMCET 2020 Hard
More PYQs from AP EAMCET
- If \(g\left(\frac{t+1}{2 t+1}\right)=t+1\), then \(\int g(x) d x=\)AP EAMCET 2018 Medium
- A magnetic needle lying parallel to a magnetic field requires \(W\) units of work to turn it through \(60^{\circ}\). The torque required to maintain the needle in this position will beAP EAMCET 2020 Hard
- A train approaching a railway crossing at a speed of sounds a whistle of frequency , when it is away from the crossing. The frequency heard by the observer standing on the road perpendicular to the track from the crossing at a distance of is (Speed of sound in air )AP EAMCET 2019 Hard
- When 2 moles of a monatomic gas expands adiabatically from a temperature of \(80^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\), the work done is W . The work done when 3 moles of a diatomic gas expands adiabatically from \(50^{\circ} \mathrm{C}\) to \(20^{\circ} \mathrm{C}\), isAP EAMCET 2024 Medium
- If the lines \(3 x+y-2=0, p x+2 y-3=0\) and \(2 x-y-3=0\) are concurrent, then \(p=\)AP EAMCET 2020 Medium
- \(\int \frac{x}{\sqrt{x+1}+\sqrt{x-1}} d x=A(x)(x+1)^{\frac{3}{2}}+B(x)(x-1)^{\frac{3}{2}}+C\) , then \(A(x)+B(x)=\)AP EAMCET 2019 Hard