Complex Numbers

  • Thread starter craig100
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  • #1
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Hello guys;
I'm after a bit of help here, I may have missed something completely obvious, but I can't seem to figure out the working of:

1 + i = √2(cos π/4+ i sin π/4)

ie; How does 1 + i equal √2(cos π/4+ i sin π/4)??

any help would be appreciated;
Thanks
Craig :)
 

Answers and Replies

  • #2
1,631
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1 + i = √2(cos π/4+ i sin π/4)

ie; How does 1 + i equal √2(cos π/4+ i sin π/4)??

Craig :)

what do these litle squares stand for? what are those symbols, what do they represent??
 
  • #3
2,063
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what do these litle squares stand for? what are those symbols, what do they represent??
I'm glad that I'm not the only seeing those squares. :biggrin: Some problem with fonts, I suppose.
 
  • #4
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Sorry, I guess you don't have those fonts installed on your system...i'll put it a different way;

1 + i = root(2) . (cos(pi/4) + i.sin(pi/4))

pi ...being pi(3.14...) :P

so my question is how does (1 + i) equal the value above?

I hope thats clearer?

Craig :)
 
  • #5
Gib Z
Homework Helper
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Any complex number can be expressed in the form a+bi.

In this case, a=1 and b=1.
Complex numbers can be expressed in the following form:
[tex]r(\cos x + i\sin x)[/tex] where [itex]r=\sqrt{a^2+b^2}[/itex] and x is arctan (b/a). Anything you don't understand or want more info on im right here.
 
  • #6
Gib Z
Homework Helper
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Ok picture a plane where one unit on the y axis is 1 unit on the imaginaries, or x units "up" is xi. And the x axis is just the real number line. So to denote a+bi, we would have a point that is a units from the origin to the right, and b units up. Or co ordinates, (a,b).
 
  • #7
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Craig,
Plot the complex number on an Argand Plane. Find it's real and imaginary components in terms of the angle it makes with the real axis, and it's modulus.
 
  • #8
Gib Z
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Yup what neutrino said :D
 
  • #9
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ahh, thanks guys...its been a while since I have done complex numbers, I understand it now :smile:, thanks for the quick and informative replies.

Craig :biggrin:
 

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