1.What figure complex roots of this equation create $$z^4+16z^2+100=0$$
2.What are the equations of straight lines that link vertexes of this figure
I don't know how to proceed
$z^2=x$ , $x^2+16x+100=0$ , $\delta=-144=144i^2$ ,$\sqrt{\delta}=12i$ ,
$x_1^2=\dfrac{ -16-12i}{4}=\sqrt{-4-3i} ,\:x_2^2=\dfrac{ -16+12i}{4}=\sqrt{-4+3i}$.
The second part of this task is to rotate 90 degrees said figure and find vertexes using a) complex numbers b) rotation matrix
$$x_1^2=-4-3i$$
Let $x_1=a+bi$ so $$-4-3i =(a+bi)^2=a^2-b^2+2abi$$
so $2ab =-3$ and $a^2-b^2=-4$. Now solve this system if $a,b$ are real...