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Is it right? \begin{equation}\overline{(-1+i)} = (1-i) \\ \sqrt[4]{-625} = \pm5i \end{equation}
And what does n in this equation means? \begin{equation}z = -\sqrt2 -\sqrt2i \\n= 9\end{equation} Is it some sort of misunderstanding or am I missing something?

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Note that $\overline{(-1+i)}$ is actually $-1-i$, not $1-i$. – Stefan Geschke Feb 29 '12 at 21:17
There's not enough information in your question to figure out what $n$ means. Could you explain what you're working on? – Jonas Kibelbek Feb 29 '12 at 21:29
up vote 4 down vote accepted

$$ \overline{-1+i} = -1-i $$

The complex conjugate flips the sign of the imaginary part.

To find the nth root of a number, express in polar form first. The rest should be simple. You can easily check your answer by taking your result to the 4th power and seeing if it agrees.

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