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Equation of straight line joining complex no p and iq(where $p,q\in R$ and $p,q\neq 0)$ is :

$\begin{array}{1 1}(A)\;z(p+iq)+\overline{z}(p-iq)=2pq\\(B)\;z(p-iq)+\overline{z}(p+iq)=2(p^2+q^2)\\(C)\;z(\large\frac{1}{p}-\frac{i}{q})+\overline{z}(\large\frac{1}{p}+\frac{i}{q})=2\\(D)\;\text{None of these}\end{array} $

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The equation of line joining p and iq is :
$\begin{vmatrix}z&\overline{z}&1\\p&p&1\\iq&-iq&1\end{vmatrix}=0$
$\Rightarrow z(p+iq)-\overline{z}(p-iq)-2ipq=0$
$\Rightarrow z(\large\frac{1}{p}-\frac{i}{q})+\overline{z}(\large\frac{1}{p}+\frac{i}{q})$$=2$
Hence (C) is the correct answer.
answered Apr 10, 2014 by sreemathi.v
 

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