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Question

Find the roots of given equation:

z33z2+6z4=0

A
1,1+3i,13i
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B
1,1+2i,12i
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C
3,1+3i,13i
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D
All of them
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Solution

The correct option is A 1,1+3i,13i
In this case, for

p(z)=z33z2+6z4,

we have that p(1)=0.

Therefore, we can factorize it further and get

z33z2+6z4=(z1)(z22z+4)

=(z1)((z1)2+3).

Their roots are just

z1=1, z2=1+i3, z3=1i3.

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