MATH135 Study Guide - Final Guide: Diophantine Equation, Joule

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: All

Document Summary

Winter 2005: (a) determine the complete solution to the linear diophantine equation. 391x + 253y = 2760. (b) suppose that the complete solution to a linear diophantine equation is given by x = 23 3n, 2i and z2 = 5 + 5 compute z1 z2 using multiplication in standard form. Give the exact result in standard form (e. g. (b) express z1 and z2 in polar form. (c) calculate z1 z2 using multiplication in polar form. Convert your result to standard form and show that it matches your result in (a). 3i: (a) prove that for r and n n, (b) find all complex 8th roots of 81i. 7 is irrational: (a) state the conjugate roots theorem. (b) given that 3 i is a complex root of the polynomial j(x) = x4 + 4x3 21x2 74x + 290, 2 + i sin : mark each statement as true or false.