Help me solve a complex cos equation

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Hello has all
I seek the solution of this equation.
cos(x+iy)= a+ib with a and b are given (and x,y,a,b are real) .

- how can one find x and y.
- has which condition I have the place to make :

x+iy= ±acos(a+ib ) +2πm

thank you well
 

Re: cos complex

The most straightforward way is to make use of Euler's Formula. See Euler's formula - Wikipedia, the free encyclopedia

Basically, we can decompose a cos into a sum of complex exponentials:

\[\cos(w) = \frac{e^{iw}+ e^{-iw}}{2}\]

So just plug in "x + iy" for "w" and find the real and imaginary parts to equate with "a" and "b", respectively.
 

Re: cos complex

there is another method to solve it ...
cos(x + jy) = cos(x).cos(jy) - sin(x).sin(jy)
= cos(x).cosh - j.sin(x).sin = a +j.b

=> cos(x).cosh = a, and sin(x).sin = -b
you can solve them to obtain final result.
 

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