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Unread 20 Apr 2004, 20:39   #1
'|'empest
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[Maths] another complex number problem

Let Rǿ denote a roation about the origin, anti-clockwise through an angle of ǿ radians.

Find the real and imaginary parts of R(5¶ / 6) (8 + 5i)


The fact that the angle comes out unfriendly looking leads me to believe i'm going at this the wrong way
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Unread 20 Apr 2004, 21:38   #2
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Re: [Maths] another complex number problem

z = (8 + 5i)
r = sqrt( 8^2 + 5^2 ) = sqrt( 89 )
tan(theta) = y/x = 5/8
theta = 32.0054degrees = 0.5586radians

z = sqrt(89)cos(0.5586) + i*sqrt(89)sin(0.5586)

z' = sqrt(89)*cos(1.3919) + sqrt(89)*i*sin(1.3919)
z' = 1.6787 + 9.2834i

?

I've not done complex number stuff since last year and it was lost on me then so if that's bollocks I'm sure Quey'll shoot me down

Edit:
It seems to be bollocks
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Last edited by pablissimo; 20 Apr 2004 at 21:52.
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Unread 20 Apr 2004, 21:59   #3
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Re: [Maths] another complex number problem

z' = -0.32 - 9.4i is what i seem to have atm...
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Unread 20 Apr 2004, 21:59   #4
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Re: [Maths] another complex number problem

Then it appears that my edit is accurate.
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Unread 20 Apr 2004, 22:00   #5
'|'empest
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Re: [Maths] another complex number problem

not necessarily, i'm ****ing shit
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Unread 20 Apr 2004, 22:52   #6
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Re: [Maths] another complex number problem

Quote:
Originally Posted by '|'empest
R(5¶ / 6)
what is that bizarre-looking character after the 5 meant to be?
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Unread 20 Apr 2004, 22:52   #7
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Re: [Maths] another complex number problem

pi
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Unread 20 Apr 2004, 22:54   #8
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Re: [Maths] another complex number problem

Oh, you must be using a different font from me. So youre wanting 8+5i rotated through 5*pi/6 yeah?
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Unread 20 Apr 2004, 22:57   #9
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Re: [Maths] another complex number problem

yup
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Unread 20 Apr 2004, 23:00   #10
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Re: [Maths] another complex number problem

multiplying 2 complex numbers together is geometrically represented by multiplying their modulus and adding their arguments. So to rotate something through 5pi/6 youd find a complex number that had 5pi/6 as its argument and 1 as its modulus and multiply by that.

ie your answer is (8+5i) * w, where w is a complex number and |w|=1, arg(w) = 5pi/6

so if w=a+bi, you have b/a = tan(5pi/6) and root(a^2 + b^2) = 1. Solve that to find a and b (and hence w), then multiply your original number by whatever you get (I dont have a calculator to hand).

Last edited by Nodrog; 20 Apr 2004 at 23:13.
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Unread 20 Apr 2004, 23:03   #11
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Re: [Maths] another complex number problem

cheers

edit : hang on.....

Last edited by '|'empest; 20 Apr 2004 at 23:08.
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Unread 20 Apr 2004, 23:16   #12
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Re: [Maths] another complex number problem

you should have a = root( 1/ ( (tan(5pi/6))^2 + 1 )), b = root(1-a^2), w=a+bi and your answer = (8+5i)*w
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Unread 20 Apr 2004, 23:18   #13
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Re: [Maths] another complex number problem

I didn't know it was pi =(( I just thought it was 5/6 =((
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Unread 20 Apr 2004, 23:20   #14
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Re: [Maths] another complex number problem

what sense does it make to rotate something through '5/6'?
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Unread 20 Apr 2004, 23:52   #15
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Re: [Maths] another complex number problem

5/6 radians or something. Espcially when it says 'R rotates by phi radians'.
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Unread 21 Apr 2004, 01:57   #16
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Re: [Maths] another complex number problem

Quote:
Originally Posted by Nodrog
what sense does it make to rotate something through '5/6'?
as much sense as it makes to rotate through 5*pi/6

PS: what i get is -9.43 -0.33i
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Last edited by at0mic.c0w; 21 Apr 2004 at 02:04.
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Unread 21 Apr 2004, 11:51   #17
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Re: [Maths] another complex number problem

Yeah, I too gets z' = -9.43 -.33i

Now that I'm adding 5pi/6 and not 5/6 an' all
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