Christian web host - 468 ARITHMETIC 4.6.4 Complex addition and multiplication can
468 ARITHMETIC 4.6.4 Complex addition and multiplication can obviously be reduced to a sequence of ordinary operations on real numbers: real + complex requires 1 addition complex + complex requires 2 additions real X complex requires 2 multiplications complex X complex requires 4 multiplications, 2 additions or 3 multiplications, 5 additions (See exercise 41. Subtraction is here considered as if it were equivalent to addition.) Therefore Horner s rule (2) uses either 472 - 2 multiplications and 3n -2 additions or 3n -1 multiplications and 6n -5 additions to evaluate U(Z) when z = z + iy is complex. Actually 2n -4 of these additions can be saved, since we are multiplying by the same number z each time. An alternative procedure for evaluating U(X + iy) is to let a1 = %, bl = w-1, r=x+x, s = x2 + y2; aj = by-1 + raj-l, bj = un–j -saj-l, l