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If z₁,z₂ and z₃ are complex number such that
|z₁|=|z₂|=|z₃|=|1/z₁ + 1/z₂ + 1/z₃|=1,then |z₁ + z₂ + z₃ | is
  • a)
    equal to 1
  • b)
    less than 1
  • c)
    greater than 3
  • d)
    equal to 3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If z₁,z₂ and z₃ are complex number such that |z₁|=|z₂|=|z₃|=|1/z₁ + 1...
Given information:
- There are three complex numbers, z₁, z₂, and z₃.
- The modulus (magnitude) of each complex number is equal to 1, i.e., |z₁| = |z₂| = |z₃| = 1.
- The modulus (magnitude) of the reciprocal of each complex number is also equal to 1, i.e., |1/z₁| = |1/z₂| = |1/z₃| = 1.

To prove:
The modulus (magnitude) of the product of the three complex numbers, |z₁z₂z₃|, is equal to 1.

Proof:
Let's consider the reciprocal of each complex number:
- Reciprocal of z₁ is 1/z₁.
- Reciprocal of z₂ is 1/z₂.
- Reciprocal of z₃ is 1/z₃.

Given that |1/z₁| = |1/z₂| = |1/z₃| = 1, we can conclude that the modulus (magnitude) of each reciprocal is equal to 1.

Now, let's consider the product of the three reciprocals: (1/z₁)(1/z₂)(1/z₃).

Since the modulus of a product is equal to the product of the moduli, we have:
|1/z₁||1/z₂||1/z₃| = 1*1*1 = 1.

Therefore, the modulus of the product (z₁z₂z₃) is also equal to 1.

Hence, the correct answer is option 'A' - |z₁z₂z₃| = 1.
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If z₁,z₂ and z₃ are complex number such that |z₁|=|z₂|=|z₃|=|1/z₁ + 1/z₂ + 1/z₃|=1,then |z₁ + z₂ + z₃ | isa)equal to 1b)less than 1c)greater than 3d)equal to 3Correct answer is option 'A'. Can you explain this answer?
Question Description
If z₁,z₂ and z₃ are complex number such that |z₁|=|z₂|=|z₃|=|1/z₁ + 1/z₂ + 1/z₃|=1,then |z₁ + z₂ + z₃ | isa)equal to 1b)less than 1c)greater than 3d)equal to 3Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If z₁,z₂ and z₃ are complex number such that |z₁|=|z₂|=|z₃|=|1/z₁ + 1/z₂ + 1/z₃|=1,then |z₁ + z₂ + z₃ | isa)equal to 1b)less than 1c)greater than 3d)equal to 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If z₁,z₂ and z₃ are complex number such that |z₁|=|z₂|=|z₃|=|1/z₁ + 1/z₂ + 1/z₃|=1,then |z₁ + z₂ + z₃ | isa)equal to 1b)less than 1c)greater than 3d)equal to 3Correct answer is option 'A'. Can you explain this answer?.
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