Complex Numbers Division (1 Viewer)

[xV1P3R]

Hi, I found this question in a textbook and was wondering how you
would divide x³-2-2i by x+1-i

The answer is
x³-2-2i = (x+1-i)[x²+(-1+i)x-2i]

I've tried turning it into a fraction and realizing the denominator, but end up with something horrible. I suppose you could manually alter the numbers so they factorize nicely, but I was wondering if there was an easier way.

Thanks

 

[annabackwards]

Do long division and factorise your quotient

 

[Drongoski]

Don't recall a general technique for doing this. But I tried a long-division approach after converting problem into:





Then do a long division: 1st you have x² + xi as 1st "multiple" which you then multiply with the divisor and you end up with:

 

[lolokay]

same as any other polynomial division isn't it?

like this sort of thing Bored of Studies - View Single Post - Quicker Method for Long Division of Polynomials
that's how I did it anyway

 

[Drongoski]

continued from above:




Next you have [-x-2i] as the next "multiple". On multiplying this with the divisor you get exactly the above "remainder". End of division.

Result of division: [x² + xi] -[x+2i]

which is equivalent to the reqd result.

 

[xV1P3R]

Oh Awesome, thanks. Long Division does look easier after realizing the denominator. Didn't quite see that before.

 

[annabackwards]

I just did the question on paper and you actually don't need to factorise the quotient or realise the denominator at all.

Click here for the solution

 

[-Onlooker-]

I just did the question on paper and you actually don't need to factorise the quotient or realise the denominator at all.

Click here for the solution

Sexy writing

 

[jchoi]

Synthetic division for me is like poo. Only because I remember I learnt it the day before one of my exams, and I failed using it in a 4 mark question out of 30 trying to save time, and actually wasted time and marks.

I'm 100% sure it's quicker and easier if you get used to it, but I suck at it! HELP ME!!! lol;