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Show that the equation \[z ^{3}+(-3+i)z^{2}+(6-3i)z+(-6-8i)=0\] has a pure imaginary root and then solve the equation. I know how to solve it by setting z=bi but what if the description would have said "has a pure real root " should i use z=a instead?

Mathematics
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yes where a is real.
Thank you, that was all :)
quickest post ever! welcome ^_^

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Other answers:

Haha yeah that troubled me a bit since I always deal with pure imaginary ones :p I assume it's the same if it doesn't have any pure root then it's z=a+bi, right?:)
right again :)
Great, thanks!
welcome ^_^

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