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

Answer»

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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