Question

Simplify the power of i.
i78
A -1
B -i
C 1
D i

Answer 1

`\\ \rm\longmapsto i^(78)`

• Divide 78 by 4

`\\ \rm\longmapsto (78)/(4)`

`\\ \rm\longmapsto (39)/(2)`

`\\ \rm\longmapsto 19(1)/(2)`

Now

remainder is 2

`\\ \rm\longmapsto i^2`

`\\ \rm\longmapsto (√(-1))^2`

`\\ \rm\longmapsto -1`

Hence

`\\ \rm\longmapsto i^(78)=-1`