H2 math (complex no.)

• th3m0ment

  2 Sep 07, 12:57

  when is apply de moivre? when power of z >3?
  
  got one question here.
  
  (1+ z^2) / (1 - z^2) = i
  
  help?
• eagle

  2 Sep 07, 14:56

  I don't like de moivre's theorem... I rather use Euler's formula... But they are interchangeable....
  
  for your question
  
  1+z^2 = i - iz^2
  
  rearranging gives u
  
  z^2 = (-1 + i) / (1 + i) --> pls check
  
  Using Euler's formula,
  -1 + i = e^(i * 3pi /4) * sqrt(2)
  1 + i = e^(i * pi/4) * sqrt(2)
  
  hence,
  
  z^2 = { e^(i * 3pi /4) } / { e^(i * pi/4) }
  
  z^2 = e^(i * pi/2)
  
  z = e^(i * pi/4) or -e^(i * pi/4)
  
  z = 1/sqrt(2) * (1 + i) or z = -1/sqrt(2) * (1 + i) --> pls check also...
• club18

  2 Sep 07, 17:45

  Originally posted by eagle:

  I don't like de moivre's theorem... I rather use Euler's formula... But they are interchangeable....
  
  for your question
  
  1+z^2 = i - iz^2
  
  rearranging gives u
  
  z^2 = (-1 + i) / (1 + i) --> pls check
  
  Using Euler's formula,
  -1 + i = e^(i * 3pi /4) * sqrt(2)
  1 + i = e^(i * pi/4) * sqrt(2)
  
  hence,
  
  z^2 = { e^(i * 3pi /4) } / { e^(i * pi/4) }
  
  z^2 = e^(i * pi/2)
  
  z = e^(i * pi/4) or -e^(i * pi/4)
  
  z = 1/sqrt(2) * (1 + i) or z = -1/sqrt(2) * (1 + i) --> pls check also...

  looks chim..
  anw, once u got to,
  z^2=( i - 1 )/( 1 + i )
  factorise to get z^2 = i
  easier..
• th3m0ment

  2 Sep 07, 20:35

  i see kudos~