AP EAMCET · Maths · Complex Number
If \((x-i y)^{1 / 3}=2-i \sqrt{3}\) and the point \(z=(x, y)\) lies on the line \(\frac{x}{2}+\frac{y}{\sqrt{3}}=k\), then \(k=\)
- A \(16\)
- B \(2\)
- C \(8\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
Given, \((x-i y)^{1 / 3}=2-i \sqrt{3}\) \(\Rightarrow \quad x-i y=(2-i \sqrt{3})^3\) \(=8+3 i \sqrt{3}-i 2 i \sqrt{3}-18\) \(\begin{aligned} & \Rightarrow \quad x-i y=-10-9 i \sqrt{3} \\ & \Rightarrow \quad x=-10 \text { and } y=9 \sqrt{3}\end{aligned}\) Thus,…
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 three sides of a triangle are given by \(\left(x^2+7 x y+2 y^2\right)(y-1)=0\). Then the centroid of that triangle isAP EAMCET 2017 Hard
- The points in the argand plane represented by the complex conjugates of \(1+2 i, 2-3 i, 3-4 i\)AP EAMCET 2019 Easy
- The distance between two parallel planes \(a x+b y+c z+d_1=0\), \(a x+b y+c z+d_2=0\) is given by \(\frac{\left|d_1-d_2\right|}{\sqrt{a^2+b^2+c^2}}\).
If the plane \(2 x-y+2 z+3=0\) has the distances \(\frac{1}{3}\) and \(\frac{2}{3}\) units from the planes \(4 x-2 y+4 z+\lambda=0\) and \(2 x-y+2 z\) \(+\mu=0\) respectively, then the maximum value of \(\lambda+\mu\) isAP EAMCET 2023 Easy - Find the angle between the planes \(x+2 y+2 z-5=0\) and \(3 x+3 y+2 z-8=0\)AP EAMCET 2020 Easy
- A question paper contains 4 questions each having 4 alternative answers. The number of ways that a candidate can answer one or more questions isAP EAMCET 2017 Medium
- If \(A\) and \(B\) be independent events with \(P(A)=\frac{1}{3}\) and \(P(B)=\frac{2}{7}\), then the value of \(P\left(\frac{A}{B^C}\right)\) isAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- If \(\alpha\) is a non-real root of the equation \(x^6-1=0\) then \(\frac{\alpha^2+\alpha^3+\alpha^4+\alpha^5}{\alpha+1}=\)AP EAMCET 2017 Hard
- Observe the following statements regarding \(\mathrm{C}_{60}\).
i. All carbons are \(s p^2\)-hybridised.
ii. It contains 12 rings of five carbons each and 20 rings of six carbons each.
iii. It is a non-aromatic compound.
iv. It is pure form of carbon.
v. \(\mathrm{C}-\mathrm{C}\) bond lengths in it are 143.5 and \(138.3 \mathrm{pm}\).
vi. It is prepared by heating graphite in an electric arc in the presence of oxygen.
The correct statements areAP EAMCET 2019 Easy - Which one of the statements, regarding X is not correct ?
3-Hydroxybutanoic acid + 3-Hydroxypentanoic acid \(\longrightarrow \mathrm{X}\)AP EAMCET 2025 Medium - If \(k_1>k_2\) are the two values of \(\mathrm{k}\) such that the lines \(y-3 k x+4=0\) and \((2 k-1) x-(8 k-1) \mathrm{y}-6=0\) are perpendicular, then the equation of the line passing through \(\left(k_1, k_2\right)\) and having the slope \(\left(\frac{k_2}{k_1}\right)\) isAP EAMCET 2017 Medium
- A coil of area is placed in a uniform magnetic field of lb. , with its plane perpendicular to the field. The coil rotates at a uniform rate to complete the revolution in . find the average emf . in the coil during intervals when the coil rotates from
i. to position
ii. to position
ii. to position
iv. to positionAP EAMCET 2020 Hard - A cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy \(E_1\) and kinetic energy of the second part is \(E_2\), relation between \(E_1\) and \(E_2\) isAP EAMCET 2014 Hard