SOLUTION: I've forgotten how to do this. ---- cos(x) = 2 Solve for x. ----------- - As an example from my book: cos(+/-arctan(2sqrt(6)/5) - i*ln(7) + n*2pi) = 10 =========== =========

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Question 1102550: I've forgotten how to do this.
----
cos(x) = 2
Solve for x.
-------------
As an example from my book:
cos(+/-arctan(2sqrt(6)/5) - i*ln(7) + n*2pi) = 10
=======================================================
--> cos(x) = 10
x = +/-arctan(2sqrt(6)/5) - i*ln(7) + n*2pi
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
There must be an error or omission in the stated problem, because
cos(x) = 2 has no solution, real or complex x.
—
—
Here is what happens if you try to solve cos(z) = 2 for z complex:
—
<— definition
Let z=a+bi where a,b are real and i is the imaginary unit

=
—
using <— Euler's equation
—
=
Now setting this last equation to 2 you get (real part is 2, imaginary part is 0) . Start by setting the imaginary part to 0:
Noting sin(-a) = -sin(a):

==> b = 0
and for the real part:

plugging in b=0, and noting cos(a) = cos(-a):

which looks like we are back to the original problem…. EXCEPT now 'a' is REAL and we know this has no solution.
—
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