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

$\\ \rm\longmapsto \dfrac{78}{4}$

$\\ \rm\longmapsto \dfrac{39}{2}$

$\\ \rm\longmapsto 19\dfrac{1}{2}$

Now

remainder is 2

$\\ \rm\longmapsto i^2$

$\\ \rm\longmapsto (\sqrt{-1})^2$

$\\ \rm\longmapsto -1$

Hence

$\\ \rm\longmapsto i^{78}=-1$