absolute value...complex numbers help?

Question

find the absolute value of | 3i/i+3|.

Answer 1

Since i is a radical, and you can't have radicals in the denominator, we need to clear that out first:

|(3i)/(i + 3)| = |(3i)(i - 3)/(i + 3)(i - 3)|
= |(3i^2 - 9i)/(i^2 - 9)|
= |(-3 - 9i)/(-1 - 9)|
= |(-3 - 9i)/(-10)|
= |(3 + 9i)/10|

And since this can never be negative, the answer is (3 + 9i)/10.

Answer 2

Well -2-4 is -6 right? so the absolute value or -6 is 6, so that would be how you do it. For the next one 5-8 is -3 right? So the absolute value would be 3. I'm sure u get it now lol