# Thread: Division of complex numbers

1. ## Division of complex numbers

If v = 3 + i and u = 2 - 5i, find the following in x + yi form.

1/v + 1/u

2. Originally Posted by Joker37
If v = 3 + i and u = 2 - 5i, find the following in x + yi form.

1/v + 1/u
This is the same as evaluating $\displaystyle \frac{\bar{v}}{v\bar{v}}+\frac{\bar{u}}{u\bar{u}}$, where $\displaystyle \bar{u}$ and $\displaystyle \bar{v}$ are the conjugates of $\displaystyle u$ and $\displaystyle v$.

Can you try to take it from here?

3. Originally Posted by Chris L T521
Can you try to take it from here?
No, really. Although your previous post above was very helpful I'd like to see a complete worked out solution. Thank you.

And, just to show you that I attempted to solve the equation:

3 - i/((3 + i)(3 - i)) + 2 + 5i/(2 - 5i)(2 + 5i)
3 - i/ (10) + 2 + 5i/29

I am not even sure this is right (I know it's incomplete). The answer is supposed to be 107/(290) + 21/(290)i

4. Originally Posted by Joker37
Anyone?... It seems that Chris L T521 is offline. I need a response as soon as possible (a reply is not strictly reserved for Chris L T521) . Thank you.
bumping is against the rules.

i think what you are saying you have is $\displaystyle \frac {3 - i}{10} + \frac {2 + 5i}{29}$ (though that is not actually what you typed)

anyway, you are right so far. now just combine the real and imaginary parts. note that you have $\displaystyle \frac 3{10} - \frac i{10} + \frac 2{29} + \frac {5i}{29}$

now continue

5. Originally Posted by Joker37
No, really. Although your previous post above was very helpful I'd like to see a complete worked out solution. Thank you.
It's very easy for us to write the complete worked out solution, but it will not be very helpful to you. That is why we try to give hints, so that you learn the thought process required for the problem.

Originally Posted by Joker37
And, just to show you that I attempted to solve the equation:

3 - i/((3 + i)(3 - i)) + 2 + 5i/(2 - 5i)(2 + 5i)
3 - i/ (10) + 2 + 5i/29

I am not even sure this is right (I know it's incomplete). The answer is supposed to be 107/(290) + 21/(290)i
You are on the right track...

Try to group all real parts together and imaginary parts together. But before that get a common denominator.

I will get you started:

$\displaystyle \frac{3 - i}{10} + \frac{2 + 5i}{29} = \frac{3 - i}{10}\times\frac{29}{29} + \frac{2 + 5i}{29}\times\frac{10}{10} = \frac{87 - 29i}{290} + \frac{20 + 50i}{290}$

Now you are just one step away from the answer... What will you do next?

Good luck

6. = 107 + 21i/290

Thanks guys!

EDIT: I'm sorry for writing the problem the wrong way. I apologize for that.