Mathematics: Post your doubts here!

[Suchal Riaz]

Here I attach my explanation (thanks to hamza.k143 who explained it to me):

My only remaining doubt is why or how do we know the line AB intersects at y= -1 (-i), because after that the rest is reasonably easy, its just that assumption I don´t get. So if anyone knows please let me know.

well it is difficult to me to grasp this. but i think it's like this: the point on the circle(which will be w for which the |w-z| is least) and it's distance from the half line has to be minimum. lets call the point X. the line X to the half line is the length we want to find. we don't know what is X and where is will but the half line.
now we need to realise that X will cut half line making 90 degree with it. and the same will happen to the point on half line. it will cut the circle at 90 degree(normal to the point X) the normal to the circumference goes through the centre of the circle. in this case the centre of circle if -i
it was a very difficult question. and i still don't know how this will come into the mind of the candidate in the exams.
maybe i am just an As student thats why i looks difficult to me.

 

[Namehere]

LOL you are on AS and you are doing A2 questions?

 

[Suchal Riaz]

LOL you are on AS and you are doing A2 questions?

i can do most of A2 math. except vectors.

 

[Namehere]

well it is difficult to me to grasp this. but i think it's like this: the point on the circle(which will be w for which the |w-z| is least) and it's distance from the half line has to be minimum. lets call the point X. the line X to the half line is the length we want to find. we don't know what is X and where is will but the half line.
now we need to realise that X will cut half line making 90 degree with it. and the same will happen to the point on half line. it will cut the circle at 90 degree(normal to the point X) the normal to the circumference goes through the centre of the circle. in this case the centre of circle if -i
it was a very difficult question. and i still don't know how this will come into the mind of the candidate in the exams.
maybe i am just an As student thats why i looks difficult to me.

I don´t get "it will cut the circle at 90 degree(normal to the point X) the normal to the circumference goes through the centre of the circle."

Or are we supposed to know that? How? Why?

 

[Namehere]

i can do most of A2 math. except vectors.

How old are you? Did you teach youself A2 or what? What exams are you sitting this summer?

 

[Suchal Riaz]

I don´t get "it will cut the circle at 90 degree(normal to the point X) the normal to the circumference goes through the centre of the circle."

Or are we supposed to know that? How? Why?

it makes sense. if there is a point X and a line AB, the shortest distance will be normal to the line AB.
so the shortest distance between circle and the line would be where tangent to the circle is parallel to the half line. so their distance is perpendicular to both half-line and circle.
if you want to know why the line from circle to half-line would represent w-z, then this might help:

we don't know exactly what is w and z, these locus are possibilities of w and z

so these purple lines represent w-z

the shortest possible line would be where the tangent to the circle. (just an intuition with no proof as it is visible from the sketch)

it will pass through the centre because:

radius makes 90 to tangent and normal makes 90 to tangent. so they both can be thought of as a straight line, passing through centre.

 

[Suchal Riaz]

How old are you? Did you teach youself A2 or what? What exams are you sitting this summer?

I'm sixteen. i am doing M1 and P1 this year.
I taught myself P3 for fun

 

[Hassan Ali Abid]

I'm sixteen. i am doing M1 and P1 this year.
I taught myself P3 for fun

Didnt you teach complex numbers to yourself ??? especially the complex no.questions which are in nov 13 papers ???

 

[Namehere]

it makes sense. if there is a point X and a line AB, the shortest distance will be normal to the line AB.
so the shortest distance between circle and the line would be where tangent to the circle is parallel to the half line. so their distance is perpendicular to both half-line and circle.
if you want to know why the line from circle to half-line would represent w-z, then this might help:
View attachment 39130
we don't know exactly what is w and z, these locus are possibilities of w and z
View attachment 39131
so these purple lines represent w-z
View attachment 39132
the shortest possible line would be where the tangent to the circle. (just an intuition with no proof as it is visible from the sketch)
View attachment 39133
it will pass through the centre because:
View attachment 39134
radius makes 90 to tangent and normal makes 90 to tangent. so they both can be thought of as a straight line, passing through centre.

Thank you soo much for your effort and time. However, I still dont full get why it passes through the centre. I mean, is there a rule for when a line passes through the centre of a circle. Could you explain it in mathematical terms please? I mean, "radius makes 90 to tangent and normal makes 90 to tangent. so they both can be thought of as a straight line, passing through centre." How does that "prove" it passes through the centre?

I hope you understand what im trying to say.

Thank youu!!

 

[asd]

Four families go to a theme park together. Mr and Mrs Lin take their 2 children. Mr O'Connor take his 2 children. Mr and Mrs Ahmed take their 3 children. Mrs Burton take her son. The 14 people all have to go through a turnstile one a a time to enter the theme park.
In how many different orders can the 8 children and 6 adults go through the turnstile if no two adults go consecutively?
Ans is 2438553600 (8! x 9 x 8 x 7 x 6 x 5 x 4)
How and Why?

 

[periyasamy]

Hi guys,need help in solving an equation
sqr root of (-2+2sqr root 3i)
The answer is +-(1+i sqr root3)
Thank u

 

[periyasamy]

Anyone can help me with this question.thanks a lot
Question may june 03(5 part 2)paper 4
http://papers.xtremepapers.com/CIE/...hematics (9709)/9709_s03_ms_1+2+3+4+5+6+7.pdf

 

[Lostsoul]

May june 2008 paper 3 qstn8 and qsrn 5. Detailed ans pls

 

[Suchal Riaz]

Thank you soo much for your effort and time. However, I still dont full get why it passes through the centre. I mean, is there a rule for when a line passes through the centre of a circle. Could you explain it in mathematical terms please? I mean, "radius makes 90 to tangent and normal makes 90 to tangent. so they both can be thought of as a straight line, passing through centre." How does that "prove" it passes through the centre?

I hope you understand what im trying to say.

Thank youu!!

normal ALWAYS passes through the circle. it is a rule. alright?

 

[Suchal Riaz]

Didnt you teach complex numbers to yourself ??? especially the complex no.questions which are in nov 13 papers ???

i didn't solve them. only problems i face are when they ask for the man/min value of the points in locus. and yes i did teach myself everything. from add math in o level to further math in A level.

 

[abruzzi]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w12_qp_31.pdf
I need some help with qn no. 8(i and ii). Could anyone please help me understand the solutions?
Thanks

 

[Suchal Riaz]

Hi guys,need help in solving an equation
sqr root of (-2+2sqr root 3i)
The answer is +-(1+i sqr root3)
Thank u

√( r( cos(θ)+isin(θ) ) )=±√r(cos(θ/2)+isin(θ/2)).

 

[Suchal Riaz]

asma tareen

 

[Namehere]

normal ALWAYS passes through the circle. it is a rule. alright?

Okay Sir! Did you just believe it when you were told that? Should i simply believe it as well? ^^

 

[Suchal Riaz]

Okay Sir! Did you just believe it when you were told that? Should i simply believe it as well? ^^

no one told me. i realised this rule just like newton realised the priciple of theorem of calculus.