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Pure 3 help...

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louis:
Candy,
The attachment I send contains solution for your question on complex number .

candy:
what program is this?  :-\
xml doesnt work on my pc  :(

louis:
Candy,
Your question : Prove that the real part of 1 / ( Z+ 2 – i ) is a constant where
Z=2 cos a +i(1 -2 sin a )

Here is the solution :

1 / ( Z+ 2 – i )

= 1 / [ 2  cos a + i( 1 – 2 sin a) +2 –i ]

= 1 / [ 2 cos a +2 + i ( 1 – 2 sin a-1 )]

= 1  / ( 2 cos a+ 2 – 2 i sin a)

=(1/2)*   [ 1/ (cos a+ 1 – i sin a) ]

=(1/2)*   [ 1 + cos a + i sin a]  /   [ (1 + cos a) – i sin a] [( 1 + cos a) + i sin a ]

=(1/2)* [ 1 + cos a + i sin a] / [ (1 + cos a)² –( i sin a)² ]

=(1/2)* (1 + cos a+ i sin a ) /   [ 1 + 2 cos a+ cos² a+ sin² a ]

=(1/2)* (1 + cos a + i sin a ) / (  2 + 2 cos a )

=(1/4) *( 1 + cos a + i sin a ) / ( 1 +  cos  a)

=(1/4)  +   (1/4)*( i sin a)  / (  1 + cos a )

           

The real part is  1 / 4 which is a constant

mac:
Another Pure maths 2/3 question...Please help...

For (ii) i find the angles by using a sin curve rather than +/-180 or 360.
I get confused by finding angles the other way! Do examiners accept the graphical method??
What are the methods that u guys use??
please Do the first part aswell... :)

 

candy:
mac one way to remember the quadrant is : ALL(1st quadrant)...STUDENTS(2nd quadrant)...TAKE(3rd quadrant)...COFFEE(4th quadrant)

All= sin cos tan
Students: sin
Take: tan
Coffe: cos

see the attachment!  :) :)

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