I know that these answers are correct, but I don't understand how to get it using the De Moivere Theorem. Can someone please explain in detail? Thank you so much!

Step-by-step explanation:10.First, convert 1+i from Cartesian to polar.r = √(1² + 1²)r = √2θ = atan(1/1), θ in first quadrantθ = 45°Therefore:(1+i)²⁰ = (√2 (cos 45° + i sin 45°))²⁰(1+i)²⁰ = 1024 (cos 45° + i sin 45°)²⁰Now applying the De Moivre theorem:1024 (cos (20×45°) + i sin (20×45°))1024 (cos (900°) + i sin (900°))1024 (-1 + 0)-102411.Repeat the same steps from Question 10.  First, convert to polar:r = √(1² + (-1)²)r = √2θ = atan(-1/1), θ in fourth quadrantθ = 315°Therefore:(1−i)¹⁰ = (√2 (cos 315° + i sin 315°))¹⁰(1−i)¹⁰ = 32 (cos 315° + i sin 315°)¹⁰Now applying the De Moivre theorem:32 (cos (10×315°) + i sin (10×315°))32 (cos (3150°) + i sin (3150°))32 (0 − i)-32i