How Do You Calculate the Magnitude of a Complex Fractional Vector?

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Homework Help Overview

The problem involves calculating the magnitude of a complex fractional vector expressed as \(\frac{6t(-3t^2\hat{i}+\hat{j})}{(1+9t^4)^2}\). The subject area pertains to vector mathematics and magnitude calculation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss how to approach the magnitude calculation by considering simpler forms of vectors. Some suggest rewriting the fraction in a more manageable format, while others propose taking the magnitude of the numerator and denominator separately.

Discussion Status

Several participants have offered different perspectives on how to handle the fraction, indicating a productive exploration of the topic. There is no explicit consensus, but various methods and properties of vectors are being discussed to aid understanding.

Contextual Notes

The original poster expresses uncertainty due to a lack of examples in lecture notes regarding fractional vectors, which may influence their approach to the problem.

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Homework Statement


Find the magnitude of \frac{6t(-3t^2\hat{i}+\hat{j})}{(1+9t^4)^2}

Homework Equations


The Attempt at a Solution


I know how to take the magnitude for something simple like 3x \hat{i} + 8y \hat{j} + 2 z \hat{k} but not this. My lecture notes don't give me any examples of how to find the magnitude of something in the form of a fraction.
 
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If a and b are real numbers, then what is the magnitude of

a\hat{i} + b\hat{j}?

If you can answer this, then don't let the fraction confuse you - just try to rewrite it in the form

a\hat{i} + b\hat{j}
 
Take the magnitude of the top and the bottom separately and then divide them.
 
Or, use this property of vectors:
||kv|| = |k|||v||

The 6t in the numerator and the denominator are just scalars.
 
All are good suggestions but the thing to realize here is that you might be getting scared of the fraction. What is the magnitude of

{16\hat{i} \over {4}} + {{20\hat{j} \over {4}}?

How is it any different from

{16\hat{i} + {20\hat{j}} \over{4}}?
 

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