Question

evaluate:
i^19
simplify in a+bi form

Answer 1

1 = i
2 = -1
3 = -i
4 = 1

Answer 2

divide 19 by 4 and look at the remainder

Answer 3

\[i^{19}=i^{4 \cdot 4+3}\]

Answer 4

\[i^3=-i\]

Answer 5

\[\large i^{19}\]


\[\large i^{16+3}\]


\[\large i^{16}*i^3\]


\[\large (i^{4})^4*i^3\]


\[\large (1)^4*i^3\]


\[\large 1*i^3\]


\[\large 1*(-i)\]


\[\large -i\]
So \[\large i^{19}=-i\]