a Given that 1 where n Z n 1 Find the roots of the equations

Last updated: 9/12/2023

a Given that 1 where n Z n 1 Find the roots of the equations for the various values of n and complete the table below 77 3 4 5 6 7 750 51 1 Roots 73 Sum of the roots What conclusion can you make b Find the roots of the equation 1 0 where n 2 Represent these roots on the Argand 2 7 diagram Suppose w e is the root with the smallest positive argument express the other roots in terms of w Show that 1 w w w w 0 using i the sum of geometric series the expansion of z 1 1 z 2 2 c For any two complex numbers and w use the properties of a complex conjugate to establish the relationship wf z wf 2 P wf Sketch and was vectors on an Argand plane If the vectors and w form a parallelogram find the length of the diagonals of the parallelogram in terms of and w Give a geometric interpretation of