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Question

Let z be a complex number satisfying the equation z2(3+i)z+m+2i=0, where mR. Suppose the equation has a real root. The additive inverse of non-real root, is

A
1i
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B
1+i
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C
1i
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D
2
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Solution

The correct option is C 1i
z2(3+i)z+m+2i=0
Let α be the real root.
Then, α2(3+i)α+m+2i=0
(α23α+m)+i(2α)=0+i0
α2=0 and α23α+m=0
α=2 and m=2
Now, product of the roots =2(1+i)
with one root as 2
So, non-real root =1+i
Additive inverse is 1i

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