Im trying to show that z=\tan[\frac{1}{i}\log(\sqrt{\frac{1+iz}{1-iz}})]

gaitaprepeted05u

gaitaprepeted05u

Answered question

2022-04-24

Im trying to show that
z=tan[1ilog(1+iz1iz)]

Answer & Explanation

Jamison Newman

Jamison Newman

Beginner2022-04-25Added 10 answers

Your idea of writing
tanx=eixeixi(eix+eix)
is a good start. Substituting x=1ilog1+iz1iz shows that
tanx=1i1+iz1iz1iz1+iz1+iz1iz+1iz1+iz.
Mutiplying the numerator and denominator by (1+iz)(1iz) yields
tanx=1i(1+iz)(1iz)(1+iz)+(1iz)=1i2iz2=z,
which isn't as nasty a calculation as you might have feared.

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