Q. Let `'z'` be a complex number and `'a'` be a real parameter such that `z^2 + az +a^2=0` then A) locus of `z` is a pair of straight lines B) `arg(z) =+- (2pi)/3)` C) `|z|=|a|` D) All

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aruv | High School Teacher | (Level 2) Valedictorian

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`Z^2+aZ+a^2=0`

`(Z+a/2)^2=((sqrt(3)ia)/2)^2`

`Z=-a/2+-(isqrt(3)a)/2`

which rep. pair of straight line.

`|Z|=sqrt((-a/2)^2+((sqrt(3)a)/2))=|a|`

`rcos(theta)=-a/2`

`rsin(theta)=+-(sqrt(3)a)/2`

`theta=+-(2pi)/3`

arg(z)=`+-(2pi)/3`

Thus correct answer is D.

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