Question

What is the value of iota to the power 19 + iota to the power 20

Answer 1

1 - i

Explanation:

`{i}^(19) + {i}^(20) \\ \\ = {i}^(18) .i + {i}^(20) \\ \\ = {( {i}^(2) )}^(9) .i + {( {i}^(2) )}^(10) \\ \\ = {( - 1)}^(9) .i + {( - 1)}^(10) \ \\ ( \because \: {i}^(2) = - 1) \\ \\ ( - 1).i + 1 \\ \\ = - i + 1 \\ \\ = 1 - i`