In the Argand plane,the distinct roots of $1+z+z^{3}+z^{4}=0$ ($z$ is a complex number) represent vertices of

The equation $\text{Im}\left( \frac{iz - 2}{z - i} \right) + 1 = 0$,where $z \in \mathbb{C}$ and $z \neq i$,represents a part of a circle having radius equal to

$|{z_1} + {z_2}| = |{z_1}| + |{z_2}|$ is possible if

Suppose that $z_{1}, z_{2}, z_{3}$ are three vertices of an equilateral triangle in the Argand plane. Let $\alpha = \frac{1}{2}(\sqrt{3} + i)$ and $\beta$ be a non-zero complex number. The points $\alpha z_{1} + \beta, \alpha z_{2} + \beta, \alpha z_{3} + \beta$ will be

If ${z_1} = 10 + 6i$,${z_2} = 4 + 6i$ and $z$ is a complex number such that $\text{amp}\left( \frac{z - z_1}{z - z_2} \right) = \frac{\pi}{4}$,then the value of $|z - 7 - 9i|$ is equal to

$A$ circle whose radius is $r$ and centre is $z_0$,then the equation of the circle is