Solve z^5=-4sqrt{2}+4sqrt{2}i

$$z ^ { 5 } = - 4 \sqrt { 2 } + 4 \sqrt { 2 } i$$

Solve for z

$$z=2^{\frac{3}{5}}e^{\frac{11\pi i}{20}}\approx -0.23711031+1.49705558i$$

$$z=2^{\frac{3}{5}}e^{\frac{3\pi i}{20}}\approx 1.35051335+0.688120921i$$

$$z=2^{\frac{3}{5}}e^{\frac{19\pi i}{20}}\approx -1.49705558+0.23711031i$$

$$z=2^{\frac{3}{5}}e^{\frac{27\pi i}{20}}\approx -0.688120921-1.35051335i$$

$$z=\sqrt[10]{2}\left(1-i\right)\approx 1.071773463-1.071773463i$$