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Mathematics: Post your doubts here!

smzimran

smzimran

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Mustehssun Iqbal said:
Assalamu alaikum,
How to calculate argument of a complex number when it turns out to be negative?? In Q.7 part two of this past paper, the answer to argument calculated comes negative, but the answer is given in positive:
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_33.pdf
Click to expand...
In these argument questions treat them the same way you treat trigonometry angles!
First find the basic angle by ignoring the negative sign when taking tan-1
Next locate the point in the argand diagram to check in which quadrant it lies.

1st quadrant --> arg = basic angle
2nd quadrant --> arg = pie - basic angle

3rd quadrant --> arg = - (pie - basic angle) OR arg = pie + basic angle
4th quadrant --> arg = - (basic angle) OR arg = 2pie - basic angle

Hope that will help
 
Mustehssun Iqbal

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smzimran said:
In these argument questions treat them the same way you treat trigonometry angles!
First find the basic angle by ignoring the negative sign when taking tan-1
Next locate the point in the argand diagram to check in which quadrant it lies.

1st quadrant --> arg = basic angle
2nd quadrant --> arg = pie - basic angle

3rd quadrant --> arg = - (pie - basic angle) OR arg = pie + basic angle
4th quadrant --> arg = - (basic angle) OR arg = 2pie - basic angle

Hope that will help
Click to expand...
waoww. that's really helpful...
P.S. You know those two words that need to be here :p
 
Mustehssun Iqbal

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zarasattar said:
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w11_qp_31.pdf
10 b!! please help me out with this! it's urgent! :(
Click to expand...
Aplogies for the photo quality and awesome handwriting :p
You integrate by the formula ;
Area= u. v - integral of udash.v.dx
there's this method of recognising u and vdash.
" L A T E "
L for logarithm, A for airthematic, T for trignometric and E for exponential...
the letter that comes first is u and the other is vdash.
in this question, airthematic comes first, in " L A T E " and exponential second. So x square is u and e raised to the power -x is vdash.
you convert vdash into v by integrating it individually. And you differentiate u and get the value of udash. Once you've done that, record the values in the side of the page or somewhere else. In the solution, they're recorded in a box. Put these values into the formula of the Area: u.v - intetgral of udash.v.dx.
There you get another integration by parts as you get the value of 2xe^ -2 in the integral sign . That indicates you have to integrate it by parts again and repeat the method again on the thing given under the integral sign.
Then you apply the limits to the equation and get the answer.
 
aliya_zad

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What is the Perpendicular formula to find the Perpendicular distance between a point and a plane!?
 
smzimran

smzimran

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Mustehssun Iqbal said:
Aplogies for the photo quality and awesome handwriting :p
You integrate by the formula ;
Area= u. v - integral of udash.v.dx
there's this method of recognising u and vdash.
" L A T E "
L for logarithm, A for airthematic, T for trignometric and E for exponential...
the letter that comes first is u and the other is vdash.
in this question, airthematic comes first, in " L A T E " and exponential second. So x square is u and e raised to the power -x is vdash.
you convert vdash into v by integrating it individually. And you differentiate u and get the value of udash. Once you've done that, record the values in the side of the page or somewhere else. In the solution, they're recorded in a box. Put these values into the formula of the Area: u.v - intetgral of udash.v.dx.
There you get another integration by parts as you get the value of 2xe^ -2 in the integral sign . That indicates you have to integrate it by parts again and repeat the method again on the thing given under the integral sign.
Then you apply the limits to the equation and get the answer.
Click to expand...
Whats this ?
LAte and stuff, never heard of it !
 
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zarasattar

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Mustehssun Iqbal said:
Aplogies for the photo quality and awesome handwriting :p
You integrate by the formula ;
Area= u. v - integral of udash.v.dx
there's this method of recognising u and vdash.
" L A T E "
L for logarithm, A for airthematic, T for trignometric and E for exponential...
the letter that comes first is u and the other is vdash.
in this question, airthematic comes first, in " L A T E " and exponential second. So x square is u and e raised to the power -x is vdash.
you convert vdash into v by integrating it individually. And you differentiate u and get the value of udash. Once you've done that, record the values in the side of the page or somewhere else. In the solution, they're recorded in a box. Put these values into the formula of the Area: u.v - intetgral of udash.v.dx.
There you get another integration by parts as you get the value of 2xe^ -2 in the integral sign . That indicates you have to integrate it by parts again and repeat the method again on the thing given under the integral sign.
Then you apply the limits to the equation and get the answer.
Click to expand...
Hey thank you so much! this was extremely helpful! best of luck for your exam, it's going to be good inshAllah :)
 
Mustehssun Iqbal

Mustehssun Iqbal

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smzimran said:
Whats this ?
LAte and stuff, never heard of it !
Click to expand...
Some method of recognizing which one is u and which one v dash in integration by parts...
Suppose there's lnx.x and you've to integrate it.
There you have a logarithm and airthematic value. So in the word " L A T E " L (logarithm ) comes first and A(airthematic ) comes after it. So lnx(logarithimic ) is u and x(airthmatic ) is vdash.
Another example: Suppose there is cosx.2x and you have to integrate it by parts. There is one airthematic term and the other one trignometric term. In "L A T E " , A (airthemitc) comes before T (trignometric ) . So 2x becomes u and cosx becomes vdash. The letter that comes first is u and the one that comes after it is vdash.
 
smzimran

smzimran

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Mustehssun Iqbal said:
Some method of recognizing which one is u and which one v dash in integration by parts...
Suppose there's lnx.x and you've to integrate it.
There you have a logarithm and airthematic value. So in the word " L A T E " L (logarithm ) comes first and A(airthematic ) comes after it. So lnx(logarithimic ) is u and x(airthmatic ) is vdash.
Another example: Suppose there is cosx.2x and you have to integrate it by parts. There is one airthematic term and the other one trignometric term. In "L A T E " , A (airthemitc) comes before T (trignometric ) . So 2x becomes u and cosx becomes vdash. The letter that comes first is u and the one that comes after it is vdash.
Click to expand...
Oh, thats a good strategy but i never need help in that i am always able to decide that but that may come of aid, so i will memorise it!
(y)
 
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