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MathsEasyAssertion Reasoning2012 · 07 May Online

Q62.Let Z1 and Z2 be any two complex number. Statement 1: |Z1 −Z2| ≥|Z1| −|Z2| Statement 2: |Z1 + Z2| ≤|Z1| + |Z2| (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is false, Statement 2 is true.

What This Question Tests

This question tests the fundamental triangle inequalities for complex numbers. Statement 2 is the standard triangle inequality, and Statement 1 is a direct consequence of it.

Concepts Tested

Modulus of complex numbersTriangle inequality for complex numbers

Formulas Used

|z1 + z2| ≤ |z1| + |z2|

||z1| - |z2|| ≤ |z1 - z2|

📚 NCERT Sections This Tests

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