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LoginH2 math (complex no.)
4 posts
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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...
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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..
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kudos~
