COMEDK · Maths · 3. Complex Number
If the conjugate of \((x+i y)(1-2 i)\) be \(1+i\), then
- A \(x-i y=\dfrac{1-i}{1+2 i}\)
- B \(x+i y=\dfrac{1-i}{1-2 i}\)
- C \(y=\dfrac{3}{5}\)
- D \(x=\dfrac{1}{5}\)
Answer & Solution
Correct Answer
(B) \(x+i y=\dfrac{1-i}{1-2 i}\)
Step-by-step Solution
Detailed explanation
Given the conjugate of \((x+iy)(1-2i)\) is \(1+i\). Let \(z = (x+iy)(1-2i)\). Then \(\overline{z} = 1+i\). Taking the conjugate on both sides, \(z = \overline{1+i} = 1-i\). Thus, \((x+iy)(1-2i) = 1-i\). Dividing by \((1-2i)\), we get \(x+iy = \dfrac{1-i}{1-2i}\). To simplify,…
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
- Given the matrices \(A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 2 \end{bmatrix}\) and \(B = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 1 & 2 \\ 0 & 2 & 1 \end{bmatrix}\), then the minor \(M_{23}\) of the matrix \((A B^{-1})^{-1}\) is:COMEDK 2026 Medium
- If the lines \(x+3 y-9=0,4 x+b y-2=0\) and \(2 x-y-4=0\) are concurrent, then \(b=\)COMEDK 2016 Easy
- \(\left(\cos \dfrac{\pi}{12}-\sin \dfrac{\pi}{12}\right)\left(\tan \dfrac{\pi}{12}+\cot \dfrac{\pi}{12}\right)=\)COMEDK 2024 Easy
- \(2^{3 n}-7 n-1\) is divisible byCOMEDK 2021 Easy
- A straight line makes positive intercepts on the coordinate axes whose sum is 5 . If the line passes through the point \(P(-3,4)\) then the equation of a line isCOMEDK 2025 Medium
- If \(1+i=(x+i y)(u+i v)\), then \(\tan ^{-1}\left(\frac{y}{x}\right)+\cot ^{-1}\left(\frac{u}{v}\right)\) has the valueCOMEDK 2014 Easy
More PYQs from COMEDK
- The scalar components of a unit vector which is perpendicular to each of the vectors \(\hat{\imath}+2 \hat{\jmath}-\hat{k}\) and \(3 \hat{\imath}-\hat{\jmath}+2 \hat{k}\) areCOMEDK 2023 Medium
- A capacitor of capacity \(2 ~\mu \mathrm{F}\) is charged upto a potential \(14 \mathrm{~V}\) and then connected in parallel to an uncharged capacitor of capacity \(5 ~\mu \mathrm{F}\). The final potential difference across each capacitor will beCOMEDK 2023 Easy
- The \(\mathrm{E}^{\circ}\) values of \(\mathrm{A} . \mathrm{B}\) and \(\mathrm{C}\) are given. Which element/(s) is/(are) good for coating the surface of iron to prevent corrosion?
Given: \([\mathrm{E}_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^0=-0.44 \mathrm{~V} ; \quad \mathrm{E}_{\mathrm{A}^{2+} / \mathrm{A}}^0=-2.37 \mathrm{~V} ; \quad \mathrm{E}_{\mathrm{B}^{2+} / \mathrm{B}}^0=-0.15 \mathrm{~V} ; \quad \mathrm{E}_{\mathrm{C}^{2+} / \mathrm{C}}^0=+0.34 \mathrm{~V}]\)COMEDK 2024 Medium - The behaviour of real gas approaches ideal behaviour atCOMEDK 2023 Easy
- An ideal gas goes from state \(A\) to state \(B\) via three different processes as indicated in the \(p-V\) diagram.
If \(Q_1, Q_2\) and \(Q_3\) indicate the heat absorbed by the three processes and \(\Delta U_1, \Delta U_2\) and \(\Delta U_3\) indicate the change in internal energy along the three processes respectively, then
COMEDK 2023 Easy - A mass of \(10 \mathrm{~kg}\) is suspended from a spring balance. It is pulled a side by a horizontal string, so that it makes an angle of \(60^{\circ}\) with the vertical. The new reading of the balance isCOMEDK 2018 Easy