= -1
= -1
[Introduction]
Since theory of complex functions is a highly developed learning, I have no intention to deny this learning from the stage of its definition. I would just like you to understand that my explanation is also allowable.
[Definition]
Assume a unit circle with center at the origin in a complex plain.
Next, we defines a function as f(x)={a coordinate of a point on the unit circle at the argument x}.
Then, we can express,
= 
Therefore,
 |
=  |
=  |
|
=  |
Let 
= 
, where 
is a real number.
then 
=
So, we are to express this as = 
.
Note that "
" should not be explained as a constant =2.71---, but as a sign.
Thus it can be explained that 
= -1 means the coordinate of the point at the argument 
on a unit circle is -1.
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