Euler, De Moivre and a printing error

[wirefree]

to all members of the forum.

In the attached image is equation numbered 3.23 which, by the application of Euler’s Identity - called De Moivre Theorem one line below - leads to equation 3.24.

Above is an a textbook frought with errors - printing ones.

I would be highly appreciative of a confirmation of the veracity of equation 3.24, which to me doesn’t seem logically derived.wirefree

 

[jedishrfu]

It looks like there's a right brace "}" missing from the 3.24 equation just before the factor ##(r - 1/2*cos(\theta))## as that factor is multiplied against the term ##(cos({\omega*l*cos\theta}/{2*c}) - j* sin({\omega*l*cos\theta}/{2*c}))##

Also in 3.23 it looks like the ##(r +- 1/2*cos(\theta))## expressions are factors in the exponent of e and not a factor against the ##e^{(...)}## expression.

There may be other errors that I haven't spotted yet.

 

[Mark44]

It looks like there's a right brace "}" missing from the 3.24 equation just before the factor ##(r - 1/2*cos(\theta))## as that factor is multiplied against the term ##(cos({\omega*l*cos\theta}/{2*c}) - j* sin({\omega*l*cos\theta}/{2*c}))##

No, I don't think the right brace is missing. It's near the end of the following line.

Also in 3.23 it looks like the ##(r +- 1/2*cos(\theta))## expressions are factors in the exponent of e and not a factor against the ##e^{(...)}## expression.

There may be other errors that I haven't spotted yet.

Didn't check this one, so can't say.