(a) Find the real and imaginary parts of ((sqrt{3}-i)^{10}) and ((sqrt{3}-i)^{-7}). For which values of (n) is...

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(a) Find the real and imaginary parts of $(\sqrt{3}-i)^{10}$ and $(\sqrt{3}-i)^{-7}$. For which values of $n$ is $(\sqrt{3}-i)^{n}$ real?

(b) What is $\sqrt{i}$ ?

(c) Find all the tenth roots of $i$. Which one is nearest to $i$ in the Argand diagram?

(d) Find the seven roots of the equation $z^{7}-\sqrt{3}+i=0$. Which one of these roots is closest to the imaginary axis?

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A Concise Introduction To Pure Mathematics

ISBN: 9781498722926

4th Edition

Authors: Martin Liebeck

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Question Posted: May 19, 2024 12:00 PM

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(a) Find the real and imaginary parts of ((sqrt{3}-i)^{10}) and ((sqrt{3}-i)^{-7}). For which values of (n) is...

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A Concise Introduction To Pure Mathematics

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