(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let z be a complex number. I want to solve cos(z)= -i*sin(z).

3. The attempt at a solution

Here's my work:

cos(z) = -i*sin(z) implies cos(z) + isin(z) = 0.

Therefore exp(i*z) = 0. Now put z= x+iy then i*z = i*(x+iy) = ix - y, hence

exp(i*z) = exp(ix-y) = exp(ix)*exp(y) =0 but exp(y) is always nonzero so this implies

exp(i*x) = 0 hence cos(x)+i*sin(x) =0 thus cos(x)=0 and sin(x)=0 which is impossible.

So I think there are no solutions. Is this correct?

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# Homework Help: Help complex equation cos(z) = -isin(z)

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