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 ?

Options

A. locus of `z` is a pair of straight lines
B. `|z|=|a|`
C. `arg(z)=+-(2pi)/(3)`
D. None of these

Answer

D

Explanation

`(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|`