Solution 3.4:3

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A polynomial equation which has real coefficients always has complex conjugate roots. We can therefore say directly that the equation, in addition to the roots <math>z=2i</math> and <math>z=-1+i</math>, has roots <math>z=\overline{2i}=-2i</math> and <math>z=\overline{-1+i}=-1-i</math>. Because the equation is of degree 4, it does not have more than 4 roots.
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<center> [[Image:3_4_3.gif]] </center>
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The answer is thus
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{{Displayed math||<math>z = \left\{\begin{align}
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&\phantom{+}2i\,,\\[5pt]
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&-2i\,,\\[5pt]
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&-1+i\,,\\[5pt]
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&-1-i\,\textrm{.}
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\end{align} \right.</math>}}

Current revision

A polynomial equation which has real coefficients always has complex conjugate roots. We can therefore say directly that the equation, in addition to the roots \displaystyle z=2i and \displaystyle z=-1+i, has roots \displaystyle z=\overline{2i}=-2i and \displaystyle z=\overline{-1+i}=-1-i. Because the equation is of degree 4, it does not have more than 4 roots.

The answer is thus

\displaystyle z = \left\{\begin{align}

&\phantom{+}2i\,,\\[5pt] &-2i\,,\\[5pt] &-1+i\,,\\[5pt] &-1-i\,\textrm{.} \end{align} \right.

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