Answer:
Step-by-step explanation:
[tex](1+\sqrt{2} i)^{6} =[(1+\sqrt{2}i)^{2} ]^{3} \\=(1+2i^{2} +2\sqrt{2}i)^3\\=(1-2+2\sqrt{2}i)^3\\=(-1-2\sqrt{2}i)^3\\=-(1+16\sqrt{2}i^3+3*1^2*2\sqrt{2}i+3*1*8i^2)\\=-(1-16\sqrt{2}i+6\sqrt{2}i-24)\\=-(-23-10\sqrt{2}i)\\=23+10\sqrt{2}i[/tex]
