Finding Absolute Value of Complex Fractions

[Petkovsky]

Ok this is something i learned few years ago and I am a bit rusty.

So i have to find the absolute value of:

$$\frac{1 - 2i}{3 + 4i}$$ + $$\frac{i - 4}{6i - 8}$$

So first i add the two fractions and i get:

$$\frac{(1 - 2i)(6i - 8) + (i - 4)(3 + 4i)}{(3 + 4i)(6i - 8)}$$

Next i simplify and then i find the absolute value of the complex numbers above and below
Is this correct, because i have forgoten.

 

[physixguru]

First combine the two expressions into one 'a +ib' form.

 

[Petkovsky]

Ok I solved it, sorry for the stupid question

 

[HallsofIvy]

Actually you don't need to "combine the two expressions into one 'a+ ib' form in order to find the absolute value and here it may be better not to.
$$\left|\frac{a}{b}\right|= \frac{|a|}{|b|}$$
so you don't need to get rid of the "i" in the denominator.

 

[physixguru]

Actually you don't need to "combine the two expressions into one 'a+ ib' form in order to find the absolute value and here it may be better not to.
$$\left|\frac{a}{b}\right|= \frac{|a|}{|b|}$$
so you don't need to get rid of the "i" in the denominator.

I was emphasising on the basics sir.