Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersConjugate and Modulus of complex numbers
MediumIf $|a_k| < 1, \lambda_k \ge 0$ for $k = 1, 2, ..., n$ and $\lambda_1 + \lambda_2 + ... + \lambda_n = 1$,then the value of $|\lambda_1 a_1 + \lambda_2 a_2 + ... + \lambda_n a_n|$ is
- AEqual to one
- BGreater than one
- CZero
- DLess than one
Explore More
Similar Questions
If $(a+ib)(c+id)(e+if)(g+ih)=A+iB,$ then show that: $(a^{2}+b^{2})(c^{2}+d^{2})(e^{2}+f^{2})(g^{2}+h^{2})=A^{2}+B^{2}$
Medium
View SolutionIf $\alpha$ is the modulus of $z_1=4+3 i$,then a point that does not lie in the region represented by $|z-\overline{z_1}| \leq \alpha$ is
Let $z$ be a complex number such that $|z|+z=2+i$,where $i=\sqrt{-1}$. Then $|z|$ is equal to:
DifficultMHT CET 2024
View SolutionIf $m_1, m_2, m_3$ and $m_4$ respectively denote the moduli of the complex numbers $1+4 i, 3+i, 1-i$ and $2-3 i$,then the correct one,among the following is
DifficultTS EAMCET 2008
View SolutionIf $z$ is a complex number,then $z \cdot \overline{z} = 0$ if and only if
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo