Polynomials with purely imaginary coefficients?

Question

Finished a homework problem concerning polynomials with all real coefficients and why complex roots of p(z)=0 come in pairs. Curious is there is a similar situation for polynomials with all purely imaginary coefficients. I can't figure this one out.

Never used this site before. If this is incorrectly place, my apologies.

If all coefficients are purely imaginary, just factor i. – Lucian Jan 27 '15 at 01:27 — Lucian, Jan 27 '15 at 01:27

score 4 · Accepted Answer · answered Jan 27 '15 at 01:28

4

For every non-zero complex number $a$ and every polynomial $P$ the roots of $P$ and $aP$ are the same. Applying this with $a=i$ answers your question.

answered Jan 27 '15 at 01:28

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Polynomials with purely imaginary coefficients?

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