Find the roots of ${{z}^{2}}+z+2=0$. Hence, solve ${{(3w-1)}^{2}}+(1-3w)+2=0$ \((w^*)^2-w^*+2=0\

Question

Find the roots of ${{z}^{2}}+z+2=0$. Hence, solve ${{(3w-1)}^{2}}+(1-3w)+2=0$ $(w^*)^2-w^*+2=0$, where $w^*$ is the complex conjugate of $w$. $\frac{1}{{{w}^{2}}}-\frac{1}{w}+2=0$.

Accepted Answer

$z=(-1\pm i\sqrt7)/2$. (i) $w=\dfrac12\pm\dfrac{\sqrt7}{6}i$. (ii) $w=\dfrac12\pm\dfrac{\sqrt7}{2}i$. (iii) $w=(1\pm i\sqrt7)/4$.

Complex Numbers - Complex Roots of Quadratics with Real Coefficients

Complex Numbers - Complex Roots of Quadratics with Real Coefficients

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