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Let 'z' be a comlex number and 'a' be a ...

Let `'z'` be a comlex number and `'a'` be a real parameter such that `z^(2)+az+a^(2)=0`, then which is of the following is not true ?

A

locus of `z` is a pair of straight lines

B

`|z|=|a|`

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `z^(2)+az+a^(2)=0`
`impliesz=aomega`, `aomega^(2)` (where `'omega'` is non-real root of cube unity)
`implies` Locus of `z` is a pair of straight lines
and `arg(z)=arg(a)+arg(omega)` or `arg(a)+are(omega^(2))`
`impliesarg(z)=+-(2pi)/(3)`
Also, `|z|=|a||omega|` or `|a||omega^(2)|implies|z|=|a|`
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