Find value for (-1-i)^4/3 , give answer in cartesian form?

Question

can anyone show me how to do this problem?

please give as much detail to the answers as possible... i really have no idea how to do these type of problems :\

Answer 1

angle=180+45=225
norm=sqrt(2)
z=cube root(4) (cos 225*4/3 + isin 225*4/3)

z=cube root(4) (cos 300 + isin300 )

Answer 2

z = (a million-i)(rt3+i) = root3 +i - root3i +a million =(a million+rt3) + i (a million- rt3) polar sort z= r ( cos@ + i sin@ ) r cos@ = a million+rt3 rsin@ =a million-rt3 r^2 = (a million+rt3)^2 + (a million-rt3)^2 because sin^@ + cos^@ =a million = a million+3+2rt3+ a million-2rt3+3 =8 r =2rt2 cos@ =a million+rt3 / 2rt2 sin@=a million-rt3/2rt2 right here cos(pi/12)= a million+rt3/12 and sin(pi/12)=a million-rt3/2rt2 cos(pi/12)= cos(pi/4- pi/6) =cospi/4 cospi/6 +sinpi/4sinpi/6 =a million/rt2. rt3/2 +a million/rt2.a million/2 =(rt3 +a million) /2rt2 comparable way you could tutor sinpi/12