Problem

c) $3 i^{2}-14 i+16=0$

Answer

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Answer

Final Answer: The solutions to the equation \(3 i^{2}-14 i+16=0\) are \(\boxed{2}\) and \(\boxed{\frac{8}{3}}\)

Steps

Step 1 ：Given the quadratic equation in complex numbers: \(3 i^{2}-14 i+16=0\)

Step 2 ：Identify the coefficients as: \(a=3\), \(b=-14\), and \(c=16\)

Step 3 ：Substitute these values into the quadratic formula: \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

Step 4 ：Calculate the discriminant: \(D = (2+0j)\)

Step 5 ：Find the first solution: \(sol1 = (2+0j)\)

Step 6 ：Find the second solution: \(sol2 = (2.6666666666666665+0j)\)

Step 7 ：Final Answer: The solutions to the equation \(3 i^{2}-14 i+16=0\) are \(\boxed{2}\) and \(\boxed{\frac{8}{3}}\)

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