$\text{ If }{i}^2=-1\text{ then coefficient }{x}^6\text{ in the expansion of }{\left(1+x^2+x^4+x^6\right)}^3(1+ix{)}^{10}\text{ is equal to }$

$\text{ Coefficient of }{x}^6\text{ in }{\left(1+x^2\right)}^3{\left(1+x^4\right)}^3(1+ix{)}^{10}$

$\text{ =Coefficient of }{x}^{6}in\left(1+3x^2+3x^4+x^6\right)\left(1+3x^4\right){\left(1+ix\right)}^{10}$

$=\text{ Coefficient of }{x}^6\text{ in }\left(1+3x^2+6x^4+10x^6\right)\left[1-{}^{10}C_2{x}^2+{}^{10}C_4{x}^4-\dots \dots .-{}^{10}C_{10}{x}^{10}\right]$

$\left.=-\left({}^{10}\mathrm{C}_6\right)+3\left({}^{10}\mathrm{C}_4\right)+6\left(-{}^{10}\mathrm{C}_2\right)\right)+10=160$