# The maximum distance from origin to the point z satisfying the equation $\big|z+\large\frac{1}{z}\big|=a$ is

$\begin{array}{1 1}(A)\;\large\frac{1}{2}\normalsize (\sqrt{a^2+1}+a)&(B)\;\large\frac{1}{2}\normalsize (\sqrt{a^2+2}+a)\\(C)\;\large\frac{1}{2}\normalsize (\sqrt{a^2+4}+a)&(D)\;\text{None of these}\end{array}$

Let $z=r(\cos\theta+i\sin\theta)$
$\big|z+\large\frac{1}{z}\big|$$=a\Rightarrow \big|z+\large\frac{1}{z}\big|^2$$=a^2$