# Imaginary Numbers

• Dec 13th 2007, 11:47 AM
agentlopez
Imaginary Numbers
How do you simplify: (7+15i)-(14-i)

How do you find the reciprocal of: (-6-7i)/(-3+5i)
• Dec 13th 2007, 12:38 PM
Plato
$\frac{1}{{a + bi}} = \frac{{a - bi}}{{a^2 + b^2 }}$
• Dec 13th 2007, 12:49 PM
agentlopez
Quote:

Originally Posted by Plato
$\frac{1}{{a + bi}} = \frac{{a - bi}}{{a^2 + b^2 }}$

What is that supposed to mean to me regarding imaginary numbers?
• Dec 13th 2007, 12:59 PM
topsquark
Quote:

Originally Posted by agentlopez
How do you find the reciprocal of: (-6-7i)/(-3+5i)

The reciprocal of any fraction a/b is b/a. (So long as a is not 0.)

So the reciprocal of
$\frac{-6 - 7i}{-3 + 5i}$
is
$\frac{-3 + 5i}{-6 - 7i}$

Now you need to rationalize this expression. This is what Plato's comment refers to.

-Dan
• Dec 13th 2007, 12:59 PM
Plato
Quote:

Originally Posted by agentlopez
What is that supposed to mean to me regarding imaginary numbers?

Perhaps you have misunderstood the purpose of a site such as this one.
We offer help with problems; we generally do not give instruction.

You asked for help with reciprocals of complex numbers.
That is exactly what I gave you.