Statement 1: |z1−a|<a,|z2−b|<b,|z3−c|<c, where a, b, c are positive real numbers, then |z1+z2+z3| is greater than 2|a+b+c|. Statement 2: |z1±z2|≤|z1|+|z2|.
A
Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
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B
Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.
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C
Statement 1 is true and Statement 2 is false.
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D
Statement 1 is false and Statement 2 is true.
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Solution
The correct option is D Statement 1 is false and Statement 2 is true. |z1+z2+z3|=|z1−a+z2−b+z3−c+(a+b+c)| ≤|z1−a|+|z2−b|+|z3−c|+|a+b+c| ≤2|a+b+c| Hence, |z1+z2+z3| is less than 2|a+b+c|. Statement 1 is false and Statement 2 is true