Let Z1 and Z2 be any two complex number. Statement 1: |Z1-Z2| ge |Z1|-|Z2| Statement 2: |Z1+Z2| le |Z1|+|Z2|

Question

Let Z1 and Z2 be any two complex number. Statement 1: |Z1-Z2| ge |Z1|-|Z2| Statement 2: |Z1+Z2| le |Z1|+|Z2| (A) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1 (B) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1 (C) Statement 1 is true, Statement 2 is false (D) Statement 1 is false, Statement 2 is true

Tardigrade Admin · Accepted Answer

Statement -1 and 2 both are true. It is fundamental property. But Statement - 2 is not correct explanation for Statement -1.

Q. Let Z1​ and Z2​ be any two complex number. Statement 1 : ∣Z1​−Z2​∣≥∣Z1​∣−∣Z2​∣ Statement 2: ∣Z1​+Z2​∣≤∣Z1​∣+∣Z2​∣

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1

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

Statement 1 is true, Statement 2 is false

Statement 1 is false, Statement 2 is true

Statement -1 and 2 both are true. It is fundamental property. But Statement - 2 is not correct explanation for Statement -1.

Q. Let $Z_{1}$ and $Z_{2}$ be any two complex number.
Statement 1 : $∣ Z_{1} - Z_{2} ∣ \geq ∣ Z_{1} ∣ - ∣ Z_{2} ∣$
Statement 2: $∣ Z_{1} + Z_{2} ∣ \leq ∣ Z_{1} ∣ + ∣ Z_{2} ∣$

Statement -1 and 2 both are true.
It is fundamental property.
But Statement - 2 is not correct explanation for Statement -1.