Abel's theorem in problems and solutions - School of Mathematics

Solutions 151
necessarily that and consequently
i.e., and
202. This group is the direct product of the group of the real numbers
(under addition) by itself (cf., 69 and 73). The unit element (zero) is the
pair (0,0).
and
203. Let Thus
and But and
Hence Moreover we have
i.e.,
204. Let and let the required complex number
be Thus To have
the two following equations must be satisfied:
This system of equations has exactly one solution:
for which because Hence
205. Let Thus
and
from which it results that
206. We have
207. Answer.
208.
(since