MathDB

Problem 9

Part of 2019 LIMIT Category A

Problems(2)

shape in complex plane

Source: LIMIT 2019 CAS1 P9

4/28/2021
ABCDABCD is a quadrilateral on the complex plane whose four vertices satisfy z4+z3+z2+z+1=0z^4+z^3+z^2+z+1=0. Then ABCDABCD is a <spanclass=′latex−bold′>(A)</span> Rectangle<span class='latex-bold'>(A)</span>~\text{Rectangle} <spanclass=′latex−bold′>(B)</span> Rhombus<span class='latex-bold'>(B)</span>~\text{Rhombus} <spanclass=′latex−bold′>(C)</span> Isosceles Trapezium<span class='latex-bold'>(C)</span>~\text{Isosceles Trapezium} <spanclass=′latex−bold′>(D)</span> Square<span class='latex-bold'>(D)</span>~\text{Square}
complex numberscomplexalgebrageometry
last digit of 2019^2019

Source: LIMIT 2019 CAS2 P9

4/28/2021
Last digit of 201920192019^{2019} is
number theory