- #1
uman
- 352
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Hi all. What do you do when you are reading a math book and there are multiple problems you can't solve in a chapter?
For example, I am trying to learn from Apostol's book "Mathematical Analysis". In the problems at the end of the first chapter there are two that I haven't been able to figure out how to solve. It seems like the solution should be so simple but I'm just not seeing it. (There are two more I haven't attempted yet, but I think I can solve them.) Does this mean I'm not ready for the book and should get an easier one? Or is not being able to solve a couple problems in a chapter normal?
In case anyone's wondering, here's one of the problems I haven't been able to figure out:
Let [tex]w[/tex] be a given complex number. If [tex]w\not=\pm 1[/tex], show that there exist two values of [tex]z=x + iy[/tex] satisfying the conditions [tex]cos(z)=w[/tex] and [tex]-\pi<x\leq\pi[/tex].
The identity [tex]cos(z) = cos(-z)[/tex] says that if there is one such [tex]z[/tex], there have to be two... Other than that I'm at a loss.
For example, I am trying to learn from Apostol's book "Mathematical Analysis". In the problems at the end of the first chapter there are two that I haven't been able to figure out how to solve. It seems like the solution should be so simple but I'm just not seeing it. (There are two more I haven't attempted yet, but I think I can solve them.) Does this mean I'm not ready for the book and should get an easier one? Or is not being able to solve a couple problems in a chapter normal?
In case anyone's wondering, here's one of the problems I haven't been able to figure out:
Let [tex]w[/tex] be a given complex number. If [tex]w\not=\pm 1[/tex], show that there exist two values of [tex]z=x + iy[/tex] satisfying the conditions [tex]cos(z)=w[/tex] and [tex]-\pi<x\leq\pi[/tex].
The identity [tex]cos(z) = cos(-z)[/tex] says that if there is one such [tex]z[/tex], there have to be two... Other than that I'm at a loss.
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