Question 1043494
{{{z^4 = -2sqrt(3) - 2i}}}

<===> {{{z^4 = 4(-sqrt(3)/2 - i/2) = 4(cos(7*pi/6) + i*sin(7*pi/6)) = 4*exp(i*(7*pi)/6)}}}


===> The principal 4th root is {{{z = 4^(1/4)*exp(i*(7*pi)/24) = sqrt(2)*exp(i*(7*pi)/24)}}}


===> The other 4th roots are 

{{{r[2] = sqrt(2)*exp(i*(19*pi)/24)}}},
{{{r[3] = sqrt(2)*exp(i*(31*pi)/24)}}}, and 
{{{r[4] = sqrt(2)*exp(i*(43*pi)/24)}}}.