write in standard form- 5/(3-15i)

Question

anonymous · Answer

is it $\large \frac{-5}{3-15i} $  ???

anonymous · Answer

either way.... just multiply by the conjugate of the denominator to both top and bottom then simplify...

anonymous · Answer

okay thanks!

anonymous · Answer

what am i doing wrong?

jim_thompson5910 · Answer

Use the difference of squares rule

$$\Large (x-y)(x+y) =x^2-y^2$$

to say that

$$\Large (3-15i)(3+15i) =3^2 - (15i)^2$$

$$\Large (3-15i)(3+15i) =9 - 225i^2$$

$$\Large (3-15i)(3+15i) =9 - 225(-1)$$

$$\Large (3-15i)(3+15i) =9 + 225$$

$$\Large (3-15i)(3+15i) =234$$

anonymous · Answer

that makes sense but how do i get to one of these answers?

jim_thompson5910 · Answer

The numerator becomes

$$\Large -5(3+15i) = -15 - 75i$$

So

$$\Large \frac{-5}{3-15i}$$

turns into

$$\Large \frac{-15 - 75i}{234}$$

Then what?

anonymous · Answer

Oh! It's just simplifying from there! Thank you!! :)

jim_thompson5910 · Answer

yes pretty much, tell me what you get

anonymous · Answer

-5/78 - 25/78 i

jim_thompson5910 · Answer

Good

$$\Large \frac{-5}{3-15i} = -\frac{5}{78} - \frac{25}{78}i$$

anonymous · Answer

Thanks a bunch! :)

jim_thompson5910 · Answer

sure thing