# Thread: Basic complex numbers

1. ## Basic complex numbers

Hey guys was just wondering if someone could explain why 5i/10i doesnt equal 0.5. My calculator says it is negative 0.5. Should the i's cancel each other out. Please give a detailed explanation, i cant find anything in my text books

2. Originally Posted by sanado
Hey guys was just wondering if someone could explain why 5i/10i doesnt equal 0.5. My calculator says it is negative 0.5. Should the i's cancel each other out. Please give a detailed explanation, i cant find anything in my text books
Using the "correct" method (rationalizing the denominator):
$\displaystyle \frac{5i}{10i}$

$\displaystyle = \frac{5i}{10i} \cdot \frac{-10i}{-10i} = \frac{-50i^2}{-100i^2} = \frac{50}{100} = \frac{1}{2}$
so you are putting something into your calculator wrong. (Or the calculator needs to be replaced!)

-Dan

3. Originally Posted by sanado
Hey guys was just wondering if someone could explain why 5i/10i doesnt equal 0.5. My calculator says it is negative 0.5. Should the i's cancel each other out. Please give a detailed explanation, i cant find anything in my text books
I have one word for you: BRACKETS!

You need to key in (5i)/(10i).

Your calculator will understand 5i/10i to mean 5i/10 and then multiply the result by i, which of course will give -1/2.

Calculators are very stupid things - they only do exactly what you tell them, often this not what you think you tell them.