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# p4 complex numbers watch

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1. muh!

someone help me out with question 3, ex 3c (edexcel)
what i did was times out the brackets then rationalised the denominator but 'course im missing the = -1 bit

if you dont do edexcel;

Simply without usign a calculator:
[cos(pi/7) - isin(pi/7)]^3 / [cos(pi/7) + isin(pi/7)]^4

cos(-pi) + isin(-pi) = -1
2. (Original post by kikzen)
muh!

someone help me out with question 3, ex 3c (edexcel)
what i did was times out the brackets then rationalised the denominator but 'course im missing the = -1 bit

if you dont do edexcel;

Simply without usign a calculator:
[cos(pi/7) - isin(pi/7)]^3 / [cos(pi/7) + isin(pi/7)]^4

cos(-pi) + isin(-pi) = -1
E^(-3.i.pi/7)/E^(4.i.pi/7) = E^(-3ipi/7 + 4ipi/7) = E^-ipi = -1
3. (Original post by It'sPhil...)
E^(-3.i.pi/7)/E^(4.i.pi/7) = E^(-3ipi/7 + 4ipi/7) = E^-ipi = -1
um ive never done that before; why did you do that?
4. (Original post by kikzen)
um ive never done that before; why did you do that?
e^ix = cosx + isinx . It makes problems like this a lot easier
5. (cos(pi/7)-isin(pi/7))^3/(cos(pi/7)+isin(pi/7))^4

using (cosx+isinx)^n = cos(nx)+isin(nx),

=(cos(3pi/7)-isin(3pi/7))/(cos(4pi/7)+isin(4pi/7))
=(cos(3pi/7)-isin(3pi/7))(cos(4pi/7)-isin(4pi/7))/(cos^2(4pi/7)+isin^2(4pi/7))
=cos(3pi/7)cos(4pi/7)-icos(3pi/7)sin(4pi/7)-isin(3pi/7)cos(4pi/7)-sin(3pi/7)sin(4pi/7)
=cos(3pi/7+4pi/7)-isin(4pi/7+3pi/7)
=cos(pi)-isin(pi)
=-1 + 0
=-1
6. (Original post by It'sPhil...)
e^ix = cosx + isinx . It makes problems like this a lot easier
The obvious alternative to the e^ix method is to multilpy top and bottom by (cos(pi/7) - isin(pi/7))^4
7. (Original post by Fermat)
(cos(pi/7)-isin(pi/7))^3/(cos(pi/7)+isin(pi/7))^4

using (cosx+isinx)^n = cos(nx)+isin(nx),

=(cos(3pi/7)-isin(3pi/7))/(cos(4pi/7)+isin(4pi/7))
=(cos(3pi/7)-isin(3pi/7))(cos(4pi/7)-isin(4pi/7))/(cos^2(4pi/7)+isin^2(4pi/7))
=cos(3pi/7)cos(4pi/7)-icos(3pi/7)sin(4pi/7)-isin(3pi/7)cos(4pi/7)-sin(3pi/7)sin(4pi/7)
=cos(3pi/7+4pi/7)-isin(4pi/7+3pi/7)
=cos(pi)-isin(pi)
=-1 + 0
=-1

muh i didnt see the bit in bold so i was doing some dumb **** and ended up with a silly number on the bottom..

cheers both of you !
8. (Original post by kikzen)
muh i didnt see the bit in bold so i was doing some dumb **** and ended up with a silly number on the bottom..

cheers both of you !
Btw, you don't need to worry about the e^ix stuff, cos that's Euler's theorem (P5).
9. (Original post by Nylex)
Btw, you don't need to worry about the e^ix stuff, cos that's Euler's theorem (P5).
ah no wonder

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