Question 374909
Let {{{z=x+iy}}}
Then,
{{{z^4=(x^4-6x^2y^2+y^4)+i(4x^3y-4xy^3)}}}
In this case, 
{{{x=sqrt(2)}}}
{{{y=-1}}}
{{{z^4=(4-6(2)(1)+(1))+i(4(2*sqrt(2))(-1)-4*sqrt(2)(-1))}}}
{{{z^4=(4-12+1)+i(-8*sqrt(2)+4*sqrt(2))}}}
{{{z^4=(-7)+i(-4*sqrt(2))}}}
{{{highlight(z^4=(-7)-(4*sqrt(2)))i}}}