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Q. Let `'z'` be a complex number and `'a'` be a real parameter such that `z^2 + az...

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user8235304 | Student, Grade 11 | Valedictorian

Posted August 20, 2013 at 3:45 AM via web

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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

1 Answer | Add Yours

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aruv | High School Teacher | Valedictorian

Posted August 20, 2013 at 8:22 AM (Answer #1)

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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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