Question

Simplify, Show work
1: 2i^20 + i^42
2: i^101 - i^2

Answer 1

1. i^20 X (2+i^22)

2. i² X (i¹¹-1) X (i²² + i¹¹ + 1) X (i^66 + i³³ + 1)

Explanation:

1) 2i^20 + i^42

factor out i^20

i^20 X (2 + i^22)

2) i^101 - i²

i²X(i^99-1)

i²X(i³³-1)X(i^66+i³³+1)

Using a³-b³=(a-b)(a²+ab+b²)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

I almost gave up typing. Quite stressful, but its fine