Question

Simplify the complex numbers and match them with the correct values.

Answer 1

-i, 1, i, -1, 1, -1

Explanation:

You want the simplified form of various expressions involving powers of i.

Powers of i

The definition of i is ...

i = √(-1) or i² = -1

This value can be used to find other powers:

i³ = (i²)(i) = -i

i⁴ = (i²)² = (-1)² = 1

This means any power of i is equivalent to that power modulo 4.

Application

`-i^(25)=-i^1 = \boxed{-i}\\\\i^(16)=i^0=\boxed{1}\\\\i^(17)=i^1=\boxed{i}\\\\-i^(32)=-i^0=\boxed{-1}\\\\i^(-9)* -i^(11)=-i^(-9+11)=-i^2=-(-1)=\boxed{1}\\\\(i^(23))/(-i^(11))=-i^(23-11)=-i^(12)=-i^0=\boxed{-1}`