# Dividing Complex Numbers

• Nov 4th 2008, 10:29 PM
KeiaBlake
Dividing Complex Numbers
Okay I have established that you multiply by the denomonator after changing it's sign. For example
3-2i (3-2i)(5-i)
____ = _________
5+i (5+i)(5-i)

My question is how do I solve

2+i
____
i
• Nov 4th 2008, 10:33 PM
Chris L T521
Quote:

Originally Posted by KeiaBlake
Okay I have established that you multiply by the denomonator after changing it's sign. For example
3-2i (3-2i)(5-i)
____ = _________
5+i (5+i)(5-i)

My question is how do I solve

2+i
____
i

Just multiply the numerator and denominator by i:

$\frac{2+i}{i}=\frac{2i+i^2}{i^2}=\frac{2i-1}{-1}=\color{red}\boxed{1-2i}$

Does this make sense?

--Chris