Find all the singular points of
g(z) = 1/(z^3+i)
g(z) = 1/(z^3+i)
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You need to find the values for z where the denominator is equal to zero. In other words,
z^3 + i = 0... which means
z^3 = -i = e^(3πi/2)
the cube roots are:
z = e^(πi/2), e^(πi/2 + 2πi/3), and e^(πi/2 - 2πi/3)
those come out to:
z = i
z = -√3/2 - i/2
z = √3/2 - i/2
z^3 + i = 0... which means
z^3 = -i = e^(3πi/2)
the cube roots are:
z = e^(πi/2), e^(πi/2 + 2πi/3), and e^(πi/2 - 2πi/3)
those come out to:
z = i
z = -√3/2 - i/2
z = √3/2 - i/2