Divide the following complex numbers: (6-i)/(5+4i)

(6-i)/(5+4i)=
Multiply both numerator and denominator by (5-4i):
(6-i)(5-4i)/(5+4i)(5-4i)=
(30-24i-5i+4i^2)/(5^2-16i^2)=
(30-29i+4i^2)/(25-16i^2)=
i^2 = -1
(30-29i+4×(-1))/(25-16×(-1))=
(26-29i)/41

The area for a rhombus is .  We have the area and the length of one of the diagonals, so we fill in accordingly: .  8x/2 = 4x, so now we have 16=4x.  Divide both sides by 4 to get x = 4.  It's not longer than 8, but it's the length of the other diagonal, for sure.