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

[cdotter]

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.

 

[jbunniii]

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

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

 

[╔(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

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

How is it any different from

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