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Bas_tet [7]
1 year ago
14

Find all complex solutions of the equation 2^2 − 6 + 49 = 0. Express complex numbers in the form + .

Mathematics
1 answer:
Vladimir [108]1 year ago
6 0

To find the complex solutions of the equation we use the quadratic formula:

\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(2)(49)}}{2(2)} \\ =\frac{6\pm\sqrt[]{36-392}}{4} \\ =\frac{6\pm\sqrt[]{-356}}{4} \\ =\frac{6\pm i\sqrt[]{356}}{4} \\ =\frac{6\pm i\sqrt[]{4\cdot89}}{4} \\ =\frac{6\pm i2\sqrt[]{89}}{4} \\ =\frac{3\pm i\sqrt[]{89}}{2} \end{gathered}

Therefore the solutions of the equation are:

\begin{gathered} x=\frac{3}{2}+\frac{\sqrt[]{89}}{2}i \\ \text{ or } \\ x=\frac{3}{2}-\frac{\sqrt[]{89}}{2}i \end{gathered}

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