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fp1 complex numbers

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Original post by kinderbar
it just said in the question that p>0 so i know that q=-2 :smile:


I forgot about that. But even without that information you should still be able to decide.
Original post by B_9710
I forgot about that. But even without that information you should still be able to decide.


so the other angle with the positive x-axis would be something like 3pi/4 ?
Original post by kinderbar
so the other angle with the positive x-axis would be something like 3pi/4 ?


That's right.
Original post by B_9710
That's right.


So this Newton-Raphson numerical method in solving an equation where f(x)=0 where can i not use it?
Original post by kinderbar
So this Newton-Raphson numerical method in solving an equation where f(x)=0 where can i not use it?


What do you mean, where you can't use it?
You can use it on any equation if you've got an interval or know an approximation.
Original post by Chittesh14
What do you mean, where you can't use it?
You can use it on any equation if you've got an interval or know an approximation.


That;'s what i was looking for. thanks !
Original post by kinderbar
That;'s what i was looking for. thanks !


No problem :smile:.
Original post by kinderbar
So this Newton-Raphson numerical method in solving an equation where f(x)=0 where can i not use it?


The method can fail sometimes. See 'failure analysis' on Wikipedia https://en.m.wikipedia.org/wiki/Newton%27s_method
Original post by B_9710
The method can fail sometimes. See 'failure analysis' on Wikipedia https://en.m.wikipedia.org/wiki/Newton%27s_method


Every method fails :biggrin:. All of the 3 numerical methods are unreliable but some are more than others.
I'm just happy that they're worth so many marks in the exam apparently and the questions aren't as hard as they are in the textbook, or I should say long lol.


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Original post by B_9710
The method can fail sometimes. See 'failure analysis' on Wikipedia https://en.m.wikipedia.org/wiki/Newton%27s_method


Should part (b) equal to 6root17

ImageUploadedByStudent Room1469313742.836047.jpg


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Reply 150
Original post by Chittesh14
Should part (b) equal to 6root17

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Yes it does.

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Original post by MartyO
Yes it does.

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Thanks, I knew it. The answers said 6root7 lol.


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Original post by B_9710
The method can fail sometimes. See 'failure analysis' on Wikipedia https://en.m.wikipedia.org/wiki/Newton%27s_method


Original post by MartyO
Ye



ImageUploadedByStudent Room1469317899.762688.jpg

Help part (B) please..


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(edited 7 years ago)
Original post by MartyO
Yes it does.

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HelP on post above please.


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Reply 154
a) The gradient of the normal is equal to the opposite of the inverse of the gradient of the tangent.
mtmn=1m_t \cdot m_n = -1
You have to find the derivative of the hyperbola to find the equation of the normal at P, with the vertex formula of a line (at (x1,y1)(x_1, y_1)):
yy1=m(xx1)y-y_1=m(x-x_1)
Full demo:

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b) We recall the formula for the normal at P, and have it intersect with y=xy=x. We solve for xx to find the coordinates of G.
Full demo:

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From there, it's a matter of finding the distance between P and G and square it.
d2=(x2x1)2+(y2y1)22d^2=\sqrt { (x_2 - x_1)^2 + (y_2 - y_1)^2 }^2
Full demo:

Spoiler

Original post by MartyO
a) The gradient of the normal is equal to the opposite of the inverse of the gradient of the tangent.
mtmn=1m_t \cdot m_n = -1
You have to find the derivative of the hyperbola to find the equation of the normal at P, with the vertex formula of a line (at (x1,y1)(x_1, y_1)):
yy1=m(xx1)y-y_1=m(x-x_1)
Full demo:

Spoiler

b) We recall the formula for the normal at P, and have it intersect with y=xy=x. We solve for xx to find the coordinates of G.
Full demo:

Spoiler

From there, it's a matter of finding the distance between P and G and square it.
d2=(x2x1)2+(y2y1)22d^2=\sqrt { (x_2 - x_1)^2 + (y_2 - y_1)^2 }^2
Full demo:

Spoiler



I've done part a already and got it correct. It's part b I need help on. Can you reattach the images for part b, they don't work.


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Reply 156
Original post by Chittesh14
I've done part a already and got it correct. It's part b I need help on. Can you reattach the images for part b, they don't work.


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Here:

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Reply 157
[video]http://www.examsolutions.net/maths-revision/further-maths/coordinate-geometry/parabola/tangent-normal/cartesian/example-1.php[/video]
In this video he uses implicit diff which i don't know how to do so i just square rooted both sides and used c1 diff from there to get tangents and normals but the implicit diff method gives the tangent and normal on the point (9,-12) so do i need to include all the tangents and normals?
Original post by MartyO
Here:

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Thanks man, I love you.
That question was so fkin hard.


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Original post by MartyO
Here:

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Can u help me on this too

Part b

ImageUploadedByStudent Room1469367199.868678.jpg


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