text: # Why do we take modulus of ‘i'(iota) as 1?
  
  Modulus is like magnitude. So, in case of complex numbers, we just can’t compare which number is greater and which is smaller, then how come we can say that modulus(magnitude) of ‘i’ is 1?
  
  • Lazy Eight (∞)
  1 month ago
  
  The modulus of a complex number by definition is given that z = x + iy, then |z| = √(x² + y²), where x and y are real numbers. Modulus is the distance or length of a vector.
  
  Therefore, the modulus of i is
  
  | i | = √(0 + 1²) = √1 = 1
  
  Geometrically, that makes since because you can think of i has a unit vector, so it has unit length of 1.
  
  • ?
  1 month ago
  
  i=a+bi where a=0 and b=1
  
  use the pythagorean theorem: â(a^2+b^2) which is â1=1
explanation: The document contains a math question about the modulus of the imaginary unit 'i' and includes multiple answers explaining why the modulus of 'i' is 1.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Why do we take modulus of ‘i'(iota) as 1?
  
  Modulus is like magnitude. So, in case of complex numbers, we just can’t compare which number is greater and which is smaller, then how come we can say that modulus(magnitude) of ‘i’ is 1?
  
  • Lazy Eight (∞)
  1 month ago
  
  The modulus of a complex number by definition is given that z = x + iy, then |z| = √(x² + y²), where x and y are real numbers. Modulus is the distance or length of a vector.
  
  Therefore, the modulus of i is
  
  | i | = √(0 + 1²) = √1 = 1
  
  Geometrically, that makes since because you can think of i has a unit vector, so it has unit length of 1.
  
  • ?
  1 month ago
  
  i=a+bi where a=0 and b=1
  
  use the pythagorean theorem: â(a^2+b^2) which is â1=1
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question about the modulus of the imaginary unit 'i' and includes multiple answers explaining why the modulus of 'i' is 1.
  
  Label: question-and-answer