TS EAMCET · Maths · Complex Number
The minimum value of \(|z-1|+|z-5|\) is
- A 5
- B 4
- C 3
- D 2
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \because|(z-1)-(z-5)| \leq|(z-1)|+|(z-5)| \\ & \therefore \quad|z-1-z+5| \leq|z-1|+|z-5| \\ & \Rightarrow \quad|4| \leq|z-1|+|z-5| \\ & \Rightarrow \quad|z-1|+|z-5| \geq 4 \end{aligned} \]
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 \(A\) and \(B\) are arbitrary constants, then the differential equation having \(y=A e^{-x}+B \cos x\) as its general solution isTS EAMCET 2024 Medium
- The direction cosines of the line passing through and the origin areTS EAMCET 2021 Medium
- A non-zero integer is selected randomly from the set of integers The probability that isTS EAMCET 2021 Easy
- When \(b=17\), it is found that the roots of the equation \(x^2+b x+c=0\) are -2 and -15 . If \(\alpha, \beta\) are the roots of the same equation when \(b=13\) then \(|\alpha-\beta|=\)TS EAMCET 2022 Easy
- The position vector of a point lying on the line joining the points whose positions vectors are \(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) is :TS EAMCET 2006 Easy
- \(\int \frac{x^3+2 x}{x^4+4} d x=\)TS EAMCET 2019 Easy
More PYQs from TS EAMCET
- Identify the pair of hydrides which have polymeric structureTS EAMCET 2024 Medium
- A galvanometer, having a resistance of \(50 \Omega\), gives a full scale deflection for a current of 0.05 A. The length in metre of a resistance wire of area of cross-section \(2.97 \times 10^{-2} \mathrm{~cm}^2\) that can be used to convert the galvanometer into an ammeter which can read a maximum of 5 A current is : (Specific resistance of the wire\(\left.=5 \times 10^{-7} \Omega-\mathrm{m}\right)\)TS EAMCET 2003 Hard
- Which one of the following statements is correct?TS EAMCET 2013 Medium
- If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8 , then the eccentricity isTS EAMCET 2009 Easy
- The combined equation of the three sides of a triangle is \(\left(x^2-y^2\right)(2 x+3 y-6)=0\). If the point \((0, \alpha)\) lies in the interior of this triangle, thenTS EAMCET 2016 Medium
- \(\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}\)TS EAMCET 2007 Medium