Chapter 8 - Polar Coordinates; Vectors - Section 8.3 The Complex Plane; De Moivre's Theorem - 8.3 Assess Your Understanding - Page 615: 51

$ -23+14.142i$

Based on the given conditions, we have: $(\sqrt 2-i)^6\\ \approx[\sqrt 3(cos324.7356103^\circ+i\ sin324.7356103^\circ)]^6\\ =27(cos1948.413662^\circ+i\ sin1948.413662^\circ)\\ \approx27(-0.8518518519+0.5237827994i)\\ \approx-23+14.142i$