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let r>0 -π<θ<π be real. Calculate all the values of

[tex]Re( \frac{ln(z)}{z}) [/tex]

where [tex]z=r(cos(\theta)+sin(\theta))[/tex].



Answer :

Hippalectryon
For a real z, ln(z)/z is always a real number, so the Re() is quite useless.

Thus we just need to write [tex]ln(z)/z=ln(r)+ln(\cos(\theta)+\sin(\theta))[/tex], and we can't simplify any more.

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