TS EAMCET · Maths · Complex Number
The sum of the products of the non-conjugate roots of \(i^{1 / 4}\) taken two at a time is
- A \(2\)
- B \(0\)
- C \(-1\)
- D \(-2\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
Let \(z=i^{1 / 4} \Rightarrow z^4=i=e^{i \pi / 2}\) and its roots are \(e^{i\left(\frac{\pi}{8}\right)}, e^{i\left(\frac{5 \pi}{8}\right)}, e^{i\left(\frac{9 \pi}{8}\right)}\) and \(e^{i\left(\frac{13 \pi}{8}\right)}\) and there is no pair of conjugate roots. So, sum of products…
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
- If the position vectors of \(A, B\) and \(C\) are respectively \(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}\), then \(\cos ^2 A\) is equal toTS EAMCET 2008 Medium
- The volume of the tetrahedron with \(\hat{i}-\lambda \hat{j}+\hat{k}, \lambda \hat{i}-\hat{j}-\hat{k}\) and \(\hat{i}+\hat{j}+\lambda \hat{k}\) as coterminous edges is 2 . If \(\lambda\) is an integer, then \(|\lambda \hat{\mathrm{i}}-3 \lambda \hat{\mathrm{j}}+3 \hat{\mathrm{k}}|=\)TS EAMCET 2023 Medium
- If thenTS EAMCET 2021 Easy
- If the line segment joining the points \(P(2,4,1)\) and \(Q(3,8,1)\) is divided by the plane \(3 x-k y-6 z=0\) externally in the ratio \(4: 5\), then \(k=\)TS EAMCET 2018 Easy
- If a is a unit vector, then \(|\mathbf{a} \times \hat{\mathbf{i}}|^2+|\mathbf{a} \times \hat{\mathbf{j}}|^2+|\mathbf{a} \times \hat{\mathbf{k}}|^2=\)TS EAMCET 2017 Easy
- Bag A contains 4 white and 2 black balls, bag B contains 3 white and 3 black balls and bag C contains 2 white and 4 black balls. If a bag is chosen at random and a ball is chosen at random from it, then the probability that the ball drawn is black isTS EAMCET 2022 Medium
More PYQs from TS EAMCET
- If the straight line passing through the point \(P(3,4)\) makes an angle \(\frac{\pi}{6}\) with the positive direction of \(X\)-axis and meets the line \(12 x+5 y+10=0\) at \(Q\), then the length of \(P Q\) isTS EAMCET 2020 Medium
- The Gibbs energy change of the reaction (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) corresponding to the following cell \(\mathrm{Cr}\left|\mathrm{Cr}^{3+}(0.1 \mathrm{M}) \| \mathrm{Fe}^{2+}(0.01 \mathrm{M})\right| \mathrm{Fe}\)TS EAMCET 2025 Medium
- If \(m, l, r, s, n\) are integers such that, \(9 \gt m \gt l \gt s \gt n \gt r \gt 2\) and \(\begin{aligned} & \int_{-2 \pi}^{2 \pi} \sin ^m x \cos ^n x d x=4 \int_0^\pi \sin ^m x \cos ^n x d x, \ & \int_{-\pi}^\pi \sin ^r x \cos ^s x d x=4 \int_0^{\pi / 2} \sin ^r x \cos ^s x d x \ & \text { and } \int_{-\pi / 2}^{\pi / 2} \sin ^l x \cos ^m x d x=0 \text {, the }\end{aligned}\)TS EAMCET 2024 Hard
- If \(x\) is numerically so small so that \(x^2\) and higher powers of \(x\) can be neglected, then \(\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}\) is approximately equal toTS EAMCET 2009 Easy
- The change in current through a junction diode is \(12 \mathrm{~mA}\) when the forward bias voltage is changed by \(0.6 \mathrm{~V}\). The dynamic resistance isTS EAMCET 2016 Easy
- \(\lim _{x \rightarrow \infty} x\left(\log \left(1+\frac{x}{2}\right)-\log \frac{x}{2}\right)=\)TS EAMCET 2019 Medium