Let Z_1 and Z_2 be any two complex numbers.St | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Statement $1$ is the triangle inequality for subtraction,which states $|Z_1 - Z_2| \ge ||Z_1| - |Z_2||$,and since $||Z_1| - |Z_2|| \ge |Z_1| - |Z_

Vedclass · Accepted Answer

Statement $1$ is true,Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$.

Vedclass · Answer

(B) Statement $1$ is the triangle inequality for subtraction,which states $|Z_1 - Z_2| \ge ||Z_1| - |Z_2||$,and since $||Z_1| - |Z_2|| \ge |Z_1| - |Z_2|$,Statement $1$ is true.Statement $2$ is the standard triangle inequality for addition,which is also a fundamental property of complex numbers and is true.However,Statement $2$ does not explain Statement $1$ as they are independent properties of the modulus of complex numbers.

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

Similar Questions

For any complex number $z$,$\bar{z} = \frac{1}{z}$ if and only if

The modulus of the complex number $\frac{(1+i)^2(1+3 i)}{(2-6 i)(2-2 i)}$ is

If $z_{1} = 2 - i$ and $z_{2} = 1 + i$,find $\left| \frac{z_{1} + z_{2} + 1}{z_{1} - z_{2} + 1} \right|$.

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

Let $z$ be a complex number such that $|z|+z=3+i$,where $i=\sqrt{-1}$. Then $|z|$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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