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Let z1 and z2 be any 2 complex number.Now, Statement 1:|z1 - z2| >= |z1| - |z2| Statement 2:|z1 + z2| Are both correct?And is statement 2 a correct explanation of statement 1?

Let z1 and z2 be any 2 complex number.Now,


Statement 1:|z1 - z2| >= |z1| - |z2|


Statement 2:|z1 + z2|<= |z1| + |z2|


Are both correct?And is statement 2 a correct explanation of statement 1?

Grade:12th Pass

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

Triangular Inequality:
||z_{1}|-|z_{2}|| \leq |z_{1} \pm z_{2}| \leq |z_{1}| + |z_{2}|
So
||z_{1}|-|z_{2}|| \leq |z_{1} - z_{2}|
|z_{1} + z_{2}| \leq |z_{1}| + |z_{2}|
They are true on their own.
So both statement are true independently and statement 2 is not an explanation of statement 1.
Abhishek Pachauri
35 Points
9 years ago
both are correct but statement 2 is not a correct explanation or statement 1.

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