1. ## Imaginary Numbers

How do you simplify: (7+15i)-(14-i)

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

2. $\displaystyle \frac{1}{{a + bi}} = \frac{{a - bi}}{{a^2 + b^2 }}$

3. Originally Posted by Plato
$\displaystyle \frac{1}{{a + bi}} = \frac{{a - bi}}{{a^2 + b^2 }}$
What is that supposed to mean to me regarding imaginary numbers?

4. 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
$\displaystyle \frac{-6 - 7i}{-3 + 5i}$
is
$\displaystyle \frac{-3 + 5i}{-6 - 7i}$

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

-Dan

5. 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.