The maximum value of $|z|$ where z satisfies the condition $\left| {z + \frac{2}{z}} \right| = 2$ is
$\sqrt 3 - 1$
$\sqrt 3 + 1$
$\sqrt 3 $
$\sqrt 2 + \sqrt 3 $
If for $z=\alpha+i \beta,|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation
Let $z$ and $w$ be the two non-zero complex numbers such that $|z|\, = \,|w|$ and $arg\,z + arg\,w = \pi $. Then $z$ is equal to
If $z = 3 + 5i,\,\,{\rm{then }}\,{z^3} + \bar z + 198 = $
Find the modulus and the argument of the complex number $z=-\sqrt{3}+i$
The complex numbers $sin\ x + i\ cos\ 2x$ and $cos\ x\ -\ i\ sin\ 2x$ are conjugate to each other, for