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Math Help - 4th roots of i in a +bi form

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    4th roots of i in a +bi form

    Find the fourth roots of i in a +bi form. Hint: the half angle formula may be helpful.

    Can anyone help? Thanks!
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    Quote Originally Posted by reastland View Post
    Find the fourth roots of i in a +bi form. Hint: the half angle formula may be helpful.
    First i = \exp \left( {\frac{{\pi i}}{2}} \right) so that one fourth root is \exp \left( {\frac{{\pi i}}{8}} \right).

    What are the other three?
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    It also helps to remember that there will be four fourth-roots, and they are all evenly spaced around a circle...
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    Thanks. I don't follow what you mean by "exp". Can you explain that a little further?
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    exp means e = 2.718.....
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    In other words, \displaystyle \exp{\left(\frac{\pi i}{2}\right)} = e^{\frac{\pi i}{2}}.
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    Quote Originally Posted by reastland View Post
    Thanks. I don't follow what you mean by "exp". Can you explain that a little further?
    If you are not familiar with the notation \exp(x+yi) here is an elementary way to use it.
    Think of \exp(x+yi) as r(\cos(x)+i~\sin(y)) where r=\sqrt{x^2+y^2}.

    Example: \exp(3+4i)=5(\cos(\theta)+i~\sin(\theta) where \theta=\arctan \left(\frac{4}{3}\right) .
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