SOLUTION: log (1 + cos x + i sin x)/(cos x � 1 � i sin x)

Question 14373: log (1 + cos x + i sin x)/(cos x � 1 � i sin x)
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
log
Multiplying the complex conjugate of the denominator.
Since z =
=
=
=
=
=

(polar coordinates) ...(***)
The definition of log z for complex number may be beyond your level.
Anyway,I give it here.
If the polar form for z = r ,
Here, by (***) the given z =
(where the radius r = |sin x/(cos x (1-cos x ) )|,
the argument )
Hence, the natural logarithm ln(z).
ln(z) = ln(r) + i * theta = ln|sin x| - ln|cosx (1-cos x) + i
... Answer

This is a very boring question about calculations, try your best to understand the details.

Kenny

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