Imaginary Numbers

**agentlopez** · December 13th 2007, 11:47 AM

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

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

**Plato** · December 13th 2007, 12:38 PM

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

**agentlopez** · December 13th 2007, 12:49 PM

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?

**topsquark** · December 13th 2007, 12:59 PM

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

**Plato** · December 13th 2007, 12:59 PM

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.

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