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Evaluate :

2x³+2x²-7x+72,when x=(3-5i)/2

$x = \frac{(3 - 5 i)}{2} \Rightarrow x^{2} = {\frac{(3 - 5 i)}{2}}^{2} = \frac{9 - 30 i + 25 i^{2}}{4} = \frac{9 - 25 - 30 i}{4} = \frac{- 8 - 15 i}{2} x^{3} = (\frac{3 - 5 i}{2})^{3} = \frac{{(3)}^{3} - 3 (15 i) (3 - 5 i) - (5 i)^{3}}{8} = \frac{27 - 45 i (3 - 5 i) - 125 i^{3}}{8} = \frac{27 - 135 i + 225 i^{2} + 125 i}{8} = \frac{27 - 225 - 10 i}{8} = \frac{198 i - 10 i}{8} = \frac{- 9 9 - 5 i}{4} 2 x^{3} + 2 x^{2} - 7 x + 72 = 2 (\frac{- 99 - 5 i}{4}) + 2 (\frac{- 8 - 15 i}{2}) - 7 (\frac{3 - 5 i}{2}) + 72 = \frac{- 99 - 5 i}{2} + \frac{- 16 - 30 i}{2} - \frac{21 - 35 i}{2} + 72 = \frac{- 99 - 5 i - 16 - 30 i - 21 + 35 i + 144}{2} = \frac{8}{2} = 4$

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