O-Level Additional Math

[GreenQ]

Pls help to solve this problem: Thx!!!\t


\tIf z=x+iy, find x and y for z ̅+2=i2(z-1)

[FrekiWang]

GreenQ:

Pls help to solve this problem: Thx!!!\t


\tIf z=x+iy, find x and y for z ̅+2=i2(z-1)

Your - means *(conjugate)?

I assume you mean z*+2=2i(z-1)

x-iy+2=2i(x+iy)-2i
x+2-iy=-2y+i(2x-2)

so x+2=-2y, -y=2x-2
solve, we get x=2,y=-2.

[GreenQ]

FrekiWang:

Your - means *(conjugate)?....

Thanks. The - sign is on top of z. Help pls....

[apple_a_day]

Think simple.

If you let lnx=y, it will become a simple algebra question with:

1/(2-y) - 1/(3-y) =6

Try again, my dear

[GreenQ]

Oh yes... Thank you!!

[FrekiWang]

GreenQ:

FrekiWang:

Your - means *(conjugate)?....

Thanks. The - sign is on top of z. Help pls....

I already answered your question, but I suppose in A level, we use z* rather than z(with - on top) to represent conjugate.

[babydragon]

Help needed for SEC 3 additional maths

Solve the following equations for 0deg =< (x) >= 360deg
1) cos 2(x) cos (x) = sin 4(x) sin (x)
2) cos (x) + cos 2(x) + cos 3(x) + cos 4(x) = 0

ans: 1) 30deg 45deg 90deg 135deg 150deg 210deg 225deg 270deg 315deg 330deg
2) 36deg 90deg 108deg 180deg 252deg 270deg 324deg

[justwondering]

i heard that sec sch math is going to be tough...is there any way to prepare during the hols?like ...good books to buy for sec 1? pls help :thankyou:

[BlurBerry]

justwondering:

i heard that sec sch math is going to be tough...is there any way to prepare during the hols?like ...good books to buy for sec 1? pls help :thankyou:

Last mth I bought the Casco Maths Tutor - bought for Sec 1, 2 and 3 (both A & B). Couldn't resist because we had a 30% discount voucher fm Casco (cheaper than BookFest). My son thought I was going nuts. Had to tell him that they were mainly for me to learn.

The books have explanations for the topics, some worked examples, teacher's tips, some basic drills, problem sums and some 'Thinking Skills Corner' at the end of each chapter. I guess like its title says - it is some kind of a tutor on paper.

Probably good for average students who wants to learn the basics first. For more 'advanced' students, they may find it not challenging enough.

[apple_a_day]

babydragon:

Help needed for SEC 3 additional maths

Solve the following equations for 0deg =< (x) >= 360deg
1) cos 2(x) cos (x) = sin 4(x) sin (x)
2) cos (x) + cos 2(x) + cos 3(x) + cos 4(x) = 0

ans: 1) 30deg 45deg 90deg 135deg 150deg 210deg 225deg 270deg 315deg 330deg
2) 36deg 90deg 108deg 180deg 252deg 270deg 324deg

When you handle AM Trigo, do go through the formula sheet.
Your question 1 requires you to use Double Angle formula such that sin4x=2sin2xcos2x. Factorize the cos2x, you should be able to move on.

Question 2 (look at your formula sheet!!), the only thing you can use is Factor Formula. The steps are:
1) Use Factor Formula by grouping \"cos (x) + cos 3(x)\" and \"cos 4(x) + cos 2(x) [Why: I don't like to deal with fractions]
2) Factorize 2 cos(x)
3) Use Factor Formula again and you are very near to solving.

Sorry, but my style is let people think deeper before I start to feed. So think harder again I will save you if you really really can't get it