MHT CET · Maths · Complex Number
The complex numbers \(\sin x+i \cos 2 x\) and \(\cos x-i \sin 2 x,(i=\sqrt{-1})\) are conjugate to each other for,
- A \(x=\mathrm{n} \pi, \mathrm{n} \in \mathbb{Z}\)
- B \(x=\left(\mathrm{n}+\frac{1}{2}\right) \pi, \mathrm{n} \in \mathbb{Z}\)
- C \(\mathrm{x}=(3 \mathrm{n}-1) \pi, \mathrm{n} \in \mathbb{Z}\)
- D No value of \(x\)
Answer & Solution
Correct Answer
(D) No value of \(x\)
Step-by-step Solution
Detailed explanation
\(\sin x+i \cos 2 x = \overline{(\cos x-i \sin 2 x)}\) \(\sin x+i \cos 2 x = \cos x+i \sin 2 x\)
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
- The differential equation of all circles which pass through the origin and whose centres lie on \(\mathrm{Y}\)-axis isMHT CET 2023 Medium
- The distance of the point \(\mathrm{P}(-2,4,-5)\) from the line \(\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}\) isMHT CET 2023 Easy
- The derivative of \((\log x)^{x}\) with respect to \(\log x\) isMHT CET 2010 Medium
- In a triangle \(\mathrm{ABC}, l(\mathrm{AB})=\sqrt{23}\) units, \(l(\mathrm{BC})=3\) units, \(l(\mathrm{CA})=4\) units, then \(\frac{\cot A+\cot C}{\cot B}\) isMHT CET 2024 Medium
- If \(A=\left[\begin{array}{lll}1 & 2 & 1 \\ 2 & 1 & 0\end{array}\right], B=\left[\begin{array}{ll}1 & 2 \\ 2 & 1 \\ 0 & 1\end{array}\right]\), then \((\mathrm{AB})^{-1}\) isMHT CET 2020 Easy
- If \(\mathrm{f}(x)=\frac{3 x+4}{5 x-7}\) and \(\mathrm{g}(x)=\frac{7 x+4}{5 x-3}\), then \(\mathrm{f}(\mathrm{g}(x))=\)MHT CET 2023 Easy
More PYQs from MHT CET
- The equation of motion of a particle performing linear S.H.M is \(x=5 \sin \left[4 t-\frac{\pi}{6}\right]\), where \(x\) is its displacement in \(\mathrm{cm}\). The velocity of the particle when its displacement is \(3 \mathrm{~cm}\), isMHT CET 2022 Medium
- In a game, 3 coins are tossed. A person is paid ₹150 if he gets all heads or all tails and he is supposed to pay ₹50 if he gets one head or two heads. The amount he can expect to win / lose on an average per game in ₹ isMHT CET 2025 Medium
- If \(A=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]\) such that \(A^2-4 A+3 I=0\), where \(\mathrm{I}\) is a unit matrix of order 2 , then \(A^{-1}\) isMHT CET 2022 Medium
- In the circuit shown, the potential difference across the \(4.5 \mu \mathrm{F}\) capacitor is
MHT CET 2020 Medium - Let \(\vec{v}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\bar{w}=\hat{i}+3 \hat{k}\). If \(\bar{u}\) is a unit vector, then the maximum value of the scalar triple product \([\overline{\mathrm{u}} \overline{\mathrm{v}} \overline{\mathrm{W}}]\) isMHT CET 2021 Medium
- The \(\left[\mathrm{OH}^{-}\right]\)in a solution is \(1 \times 10^{-12} \mathrm{~mol} \mathrm{dm}^{-3}\). What is the concentration of \(\mathrm{H}^{+}\)ions?MHT CET 2021 Easy