Question

The solution to the equation e2z+ez+1=0

Answer 1

$Given \: the \:equation \:e^{2z} + e^{z} + 1 = 0$

$Let \: x = e^{z} \: ---(1)$

$\implies (e^{z})^{2} + e^{z} + 1 = 0$

$\implies x^{2} + x + 1 = 0$

$If \: e^{z} = \omega \:Or \: e^{z} = \omega^{2}$

$\implies z = log_{e} \omega \:Or \: z = log_{e}\omega^{2}$

$\implies z = log_{e} \omega \:Or \: z = 2log_{e}\omega$

$Where , \omega = \frac{ -1±\sqrt{3}i}{2}$

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