# 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
The text passage contains a question about the modulus of the imaginary unit 'i' and provides multiple answers explaining why the modulus of 'i' is 1.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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
user
The text passage contains a question about the modulus of the imaginary unit 'i' and provides multiple answers explaining why the modulus of 'i' is 1.

TYPE: SINGLE_QUESTION_WITH_ANSWER