(2) Complex roots: (a) Check that z is a product of linear factors over C. (b) Check that all four of z = ±(i) satisfy z4 = -1. Confirm that z4+1 is a product of linear factors over C. (c) We know that =b±vb-4ac are the roots of az² + bz + c if a,b, c € R ±1 and z = ti all satisfy zª = 1. Confirm that z4– 1 %3D 2a -b±i/[6²–4ac[| and b2 – 4ac > 0. Check that b? – 4ac < 0. Confirm that this quadratic factors as a product of linear factors over C. are complex roots, if 2a -

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.