+37 The four complex roots of
2z4+8iz3+(−9+9i)z2+(−18−2i)z+(3−12i)=0
when plotted in the complex plane, form a rhombus. Find the area of the rhombus.
Can I have a hint?
+289 I believe that each pair of complex roots are conjugates of each other, no?
But think about it, if they are conjugates, they are mirrors across the x axis. If the distance between two roots conjuagates of each other are different from the other pair of roots which are conjugates, then this would form a trapezoid. Could you see what I mean? Can you continue from here?
What if some fo the roots are real, however? If the roots are real, what does z have to be? Is there even a root that is real? I have to go real soon, so Ill try to post the solution when I am back.
+37 @You-Know-Who, i don't think the conjugate root theorem applies here, since the coefficients are complex too.
