MACM 201 Study Guide - Quiz Guide: Dn2, The Roots

• School: Simon Fraser University
• Department: Math & Comp Sci
• Course: MACM 201
• Professor: Cedric Chauve

Document Summary

Solution: (a) the recurrence is an 4an 1 + 4an 2 = 0 so the characteristic equation is r2 4r + 4 = (r 2)2 = 0 which has just one solution r = 2. Therefore, the general solution to the recurrence is. Now we use the initial conditions on a0 and a1 to solve for c and d an = c2n + dn2n. The quadratic formula gives us the roots r = 2 4. Therefore, the general solution to the recurrence is given by the formula an = ( 1 + i)n + ( 1 i)n. Note that we are now working in the complex numbers, so here and are complex number. = (a + bi) and = (c + di) we will use our initial conditions to solve for the real numbers. 1 = a0 = (a + bi)( 1 + i)0 + (c + di)( 1 i)0. = (a + c) + (b + d)i.