ANSWER
[tex]{i}^{20} + 1 =2[/tex]
EXPLANATION
The given expression is;
[tex] {i}^{20} + 1[/tex]
Recall that, in complex numbers
[tex] {i}^{2} = - 1[/tex]
We use this identity to simplify the given expression:
[tex]{i}^{20} + 1 =( {i}^{2})^{10} + 1[/tex]
This implies that:
[tex]{i}^{20} + 1 =( - 1)^{10} + 1[/tex]
[tex]{i}^{20} + 1 =1+ 1[/tex]
[tex]{i}^{20} + 1 =2[/tex]
