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

[cdotter]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I know how to take the magnitude for something simple like [tex]3x \hat{i} + 8y \hat{j} + 2 z \hat{k}[/tex] 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.

 

[jbunniii]

If [itex]a[/itex] and [itex]b[/itex] are real numbers, then what is the magnitude of

[tex]a\hat{i} + b\hat{j}[/tex]?

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

[tex]a\hat{i} + b\hat{j}[/tex]

 

[╔(σ_σ)╝]

Take the magnitude of the top and the bottom separately and then divide them.

 

[Mark44]

Or, use this property of vectors:
||kv|| = |k|||v||

The 6t in the numerator and the denominator are just scalars.

 

[Pengwuino]

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

[tex]{16\hat{i} \over {4}} + {{20\hat{j} \over {4}}[/tex]?

How is it any different from

[tex]{16\hat{i} + {20\hat{j}} \over{4}}[/tex]?