14 CHAPTER 1 • COMPLEX NUMBERS
Because of what it erroneously connotes, it is a shame that the term imagi-
nary is used in Definition (1.6). It was coined by the brilliant mathematician and
philosopher Rene Descartes (1596-1650) during an era when quantities such as
A were thought to be just that. Gauss, who was successful in getting math-
ematicians to adopt the phrase complex number rather than imaginary number,
also suggested that they use lateral part of z in place of imaginary part of z. Un-
fortunately, that suggestion never caught on, and it appears we are stuck with
what history has handed down to us.
-------.-EXERCISES FOR SECTION 1.21. Perform the required calculations and express your answers in the form a+ bi.(a) i21s.(b} ~·
(c) Re (i).
(d) Im(2).
(e) (i-1)^3.
(f) (7 - 2i)(3i + 5).
(g) Re (7 + 6i) + Im (5 - 4i).(h) Im(~).(") 1 (4-i)(-1+2i l-3i).(j) (1 + iv'a)(i + /3).
2. Evaluate the following quantities.(a) (1 + i)(2 + i)(3 + i).
(b} (3 + i)/(2 + i).
(c) Re ((i - 1)^3 ].
(d) lm[(l + i)-^2 ).
(e) 3 -i+2< 4i _ 4-2-i 3<.
(£) (1 + i)-^2.
(g) Re ((x -iy)^2 ].(h) Im (.,~iv).