Question

Answer this question please

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Answer 1

Step-by-step explanation:

$z = - 3 + \sqrt{2} i$

${z}^{2} = ( - 3)^{2} + ( \sqrt{2} i)^{2} - 2 \times 3 \times \sqrt{2} i$

${z}^{2} = 9 - 2 - 6 \sqrt{2} i$

${z}^{2} = 7 - 6 \sqrt{2} i$

${z}^{3} = (7 - 6 \sqrt{2} i) \times ( - 3 + \sqrt{2} i)$

${z}^{3} = - 21 + 18 \sqrt{2} i + 7 \sqrt{2} i + 12$

${z}^{3} = - 9 + 25 \sqrt{2} i$

${z}^{4} = 49 - 72 - 84 \sqrt{2} i$

${z}^{4} = - 23 - 84 \sqrt{2} i$

${z}^{4} + 5 {z}^{3} + 8 {z}^{2} + 7z + 4 =$

$- 23 - 84 \sqrt{2} i + 5( - 9 + 25 \sqrt{2} i) + 8(7 - 6 \sqrt{2} i) + 7( - 3 + \sqrt{2} i) + 4$

$= - 29$