MATH 115 Fall 2019: Quiz 2 Solutions1.(a) Letz=j. Computez10in standard form using de Moivre’s Theorem.(b) Find the complex third roots of 8jin standard form. Plot these roots in the complex plane.Solution.Page 1
2. Let~u=1-2-2and~v=114.(a) Evaluate 3~u-2~v.(b) Compute~u·~v.(c) Find the exact radian measure of the angle determined by~uand~v.(d) Find a vector~w∈R3such that~wpoints in the opposite direction of~uandk~wk= 5.(e) Assume~uand~vare in standard position so that they determine two adjacent sides of a triangle.