Question

If $\left| z_{1} \right| = \left| z_{2} \right|$and $ampz_{1} + ampz_{2} = 0$, then

• A. $z_{1} = z_{2}$
• B. ${\bar{z}}_{1} = z_{2}$
• C. $z_{1} + z_{2} = 0$
• D. ${\bar{z}}_{1} = {\bar{z}}_{2}$

Answer 1

Answer: (B)

${\bar{z}}_{1} = z_{2}$

Answer 2

Sol. Let $\left| z_{1} \right| = OP,\left| z_{2} \right| = OQ$

Since amp $(z_{1})$ = $\theta$ ⇒ $amp(z_{2})$ = –$\theta$

$\because$ $Q$is point image of $P$

$\therefore$ $\overline{z_{1}} = z_{2}$

Trick : $a ⥂ rgz + a ⥂ rg\bar{z} = 0,\therefore{\bar{z}}_{1}$ must be equal to $z_{2}$.