Fp1 [ocr Mei] 2009

Yeah i did, went through it with a friend after. No problem

You should not use $j$ to represent a complex number unless you are talking about engineering, which you are not.

You need to replace $j$ with $i$ and pronto

I sat this too - got stuck on the induction question of all things, then ended up not having enough time to do the rest of the paper to my best ability, so I hope I've done OK...

I guess the key for the induction was noticing $\frac{4}{6} = 2\times3^{-1}$.

Hehe, I didn't notice that but still got it right.
I agree, compared to horrible FP2 it was nice.

Should be correct:

1. i) α = 3+ j
β = 3- j
ii) α =√10 (cos0.322 + jsin0.322)
β =√10 (cos-0.322 - jsin0.322)
2. A=2, B=1, C=5
3. i) P= ((2 1)¦(0 2))
ii) A’’ = (4,0), B’’ = (4,6), C’’ =(0,6)
iii) stretch parallel to x-axis factor 4, stretch parallel to y-axis factor 6
4 . arg(z-(2-2j)) = π/4
5. α=-2, p=-8, q=12
6. if required
7. if required
8. i) x=±√3, y=3/8
ii) x=-2,4, y=1
iii) both sections large and positive outside x =-2 and 4, with line crossing y=1 on the negative side before approaching y=1.
iv) -2<x&#8804;-&#8730;3, &#8730;3&#8804;x<4
9. i) &#945; + &#946; = 3, &#945;&#945;*= 2, (&#945;+beta)/&#945; =3/2 –(3/2)j
ii) z2 -2z +2 = 0
iii) A=-6,B=15,C=-18,D=10
10. ii) AB =42I [matrix shown]
iii) (1/42)B
iv) x =-3, y=2, z=-2

You should not use $j$ to represent a complex number unless you are talking about engineering, which you are not.

You need to replace $j$ with $i$ and pronto

I got 4 as:
arg (z-2+2j) = 50 grads
but apart from that, the rest of my answers match dr. x's

it was $\frac{\pi}{4}$, definitely.

Should be correct:
5. &#945;=-2, p=-8, q=12