If $|a_k| < 1, \lambda_k \ge 0$ 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

  • A
    Equal to one
  • B
    Greater than one
  • C
    Zero
  • D
    Less than one

Explore More

Similar Questions

The complex conjugate of $(4-3i)(2+3i)(1+4i)$ is

$(z + a)(\bar z + a)$,where $a$ is real,is equivalent to

If $\alpha_1, \alpha_2, \alpha_3$ respectively denote the moduli of the complex numbers $-i, \frac{1}{3}(1+i)$ and $-1+i$,then their increasing order is

Let $Z_1$ and $Z_2$ be any two complex numbers.
Statement $1: |Z_1 - Z_2| \ge |Z_1| - |Z_2|$
Statement $2: |Z_1 + Z_2| \le |Z_1| + |Z_2|$

$\left|\frac{1}{i^{2020}}+\frac{2}{i^{2021}}+\frac{3}{i^{2022}}+\frac{4}{i^{2023}}\right|$ is equal to

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo