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Evaluate the following: (a) For f(x) = x⁴ + 9x³ + 35x² - x + 4, find f(-5 + 4i). (b) For g(x) = x⁴ - x³ + x² + 3x - 5, find g(2 + 3i).

1. (a) -160; (b) -77 + 108i
2. (a) -160; (b) -50 + 60i
3. (a) 0; (b) 0
4. (a) 160; (b) 77 - 108i

Correct answer: (a) -160; (b) -77 + 108i

Solution

Polynomial long division by the quadratic each complex value satisfies reduces the quartic to a linear remainder, which is then evaluated.

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