Chapter 8 - Polar Coordinates; Vectors - Section 8.3 The Complex Plane; De Moivre's Theorem - 8.3 Assess Your Understanding - Page 615: 52

$ -1264-286.2167i$

Based on the given conditions, we have: $(1-\sqrt 5i)^8\\ \approx[\sqrt 6(cos294.0948426^\circ+i\ sin294.0948426^\circ)]^8\\ \approx1296(cos2352.75874^\circ+i\ sin2352.75874^\circ)\\ \approx1296(-0.975308642-0.2208462129i)\\ \approx-1264-286.2167i$