I need help confirming an equation (attached)

Question

anonymous · Answer

attachment

anonymous · Answer

The worksheet asks me to "confirm this equation".

solomonzelman · Answer

$$\color{blue}{  \frac{2-3i}{4+i}=\frac{5}{17} -\frac{4}{17}i }    $$

solomonzelman · Answer

$$\color{blue}{  \frac{2-3i}{4+i}=\frac{5}{17} -\frac{4i}{17} }    $$$$\color{blue}{  \frac{2-3i}{4+i}=\frac{5-4i}{17} }    $$

so far so god?

anonymous · Answer

The last part is 14i/17

anonymous · Answer

not 4i/17

anonymous · Answer

but yes, I understand so far

solomonzelman · Answer

$$\color{blue}{  \frac{2-3i}{4+i}=\frac{5}{17} -\frac{14i}{17} }    $$

solomonzelman · Answer

$$\color{blue}{  \frac{2-3i}{4+i}=\frac{5-14i}{17}  }    $$

anonymous · Answer

Okay

solomonzelman · Answer

cross multiply.
$$\color{blue}{ 17(2-3i)=(4+i)(5-14i)  }    $$

anonymous · Answer

Distribute?

solomonzelman · Answer

expand/simplify   each side, and tell me if they are equal or not.

yes, distribute.

anonymous · Answer

Can I solve the right side with FOIL?

solomonzelman · Answer

yes

anonymous · Answer

$$34 - 51i = 20 + -65i $$

anonymous · Answer

that's what I came up with, is that right?

solomonzelman · Answer

$$\color{blue}{  17(2-3i)=(4+i)(5-14i)  }   $$
lets do each side separately
$$\color{blue}{  17(2-3i)  }   $$$$\color{blue}{  34-51i  }   $$
now the right side,$$\color{blue}{  (4+i)(5-14i) =20-56i+5i+14 =34-51i} $$

anonymous · Answer

Wait how did you get 14 on the right side?

anonymous · Answer

I thought it was i times 14i

solomonzelman · Answer

where do I get 14, when i am simplifying the right side?
$$\color{blue}{  i \times -14i~~~->~~~-14i^2~~~->~~~14(-1)~~~->~~~14.  }   $$

anonymous · Answer

Ohhh, okay.

anonymous · Answer

Awesome!  Hey, quick question for you.

solomonzelman · Answer

Yeah?

anonymous · Answer

I'm currently doing a worksheet (I go to school online) with several problems related to this stuff.  Is there a general rule for the website about not posting a certain amount of times or something?  There's a few more I'd like help with but I don't watch to break any rules or make anyone mad.

solomonzelman · Answer

You can ask as many question as you want. Preferably, you should ask 1 question per thread. BTW - I also go to online schooling.

anonymous · Answer

Oh, cool.  What school?

solomonzelman · Answer

( Georgia )  Connections Academy.

anonymous · Answer

Cool, I've heard of that.  I go to Potter's Online Academy.

solomonzelman · Answer

Nice, good luck with the rest of your homework.

anonymous · Answer

Thanks!

solomonzelman · Answer

yw