Leaving Cert Paper Q. - Complex Numbers

td2008

Hey,

My brother is studying for maths on friday. He's having an issue with question number 15 in the pic (complex numbers) - he's getting a bit worried about his method for solving these now. Anybody familiar with these. These bring back terrible memories for me





Help appreciated

YouKnowNothing

I have the answer here, but I would be terrible at explaining it, enlighten me as to how I can post a photo from my phone please?

td2008

cheers - I've private messaged my email, if you want to post it here you can send the photo to your email, download the photo from your email to pc, go to postimage.org , upload the photo and then post the link to the thread

TheBody

There are loads of ways to do it but I'd probably proceed as follows.

Begin with the polar form and convert to the form [latex]x+iy[/latex]:

[latex]z=10\sqrt{2}(\cos(\frac{\pi}{4})+i \sin(\frac{\pi}{4}))=10+10i[/latex].

Next, we can now say that:

[latex](1+3i)(a+bi)=10+10i[/latex]. Dividing both sides by [latex](1+3i) [/latex] we get:

[latex](a+bi)=\frac{10+10i}{1+3i}[/latex].

Al that remains is to do the division on the right and then read off the values of a and b. I'll leave that job up to you!

Good luck!

td2008

Thanks for the help guys - this has helped him out.

TheBody

No problem. Glad to help!