Question

Xpower4 +4xcube +6xsquare +4x+9 if x=-1+√-2

Answer 1

Answer:

${x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 9$

$x = - 1 + \sqrt{2} i$

$x + 1 = \sqrt{2} i$

$(x + 1) {}^{2} = ( \sqrt{2} i) {}^{2}$

${x}^{2} + 2x + 1 = 2 {i}^{2} = - 2$

${x}^{2} + 2x + 3 = 0$

squaring both sides, we get

$( {x}^{2} + 2x + 3) {}^{2} = 0$

${x}^{4} + 4 {x}^{2} + 9 + 4 {x}^{ 3} + 12x + 6 {x}^{2} = 0$

${x}^{4} + 4 {x}^{3} + 10 {x}^{2} + 12x + 9 = 0$