Question

The imaginary number i raised to the Power of 38 simplifies to what ?

Answer 1

`\boxed{\bold{-1}}`

Step By Step Explanation:

Apply Exponent Rule
`\bold{a^(bc)=\left(a^b\right)^c}`

`\bold{i^(38)=\left(i^2\right)^(19)}`

`\bold{\left(i^2\right)^(19)}`

Apply Imaginary number Rule
`\bold{\:i^2=-1}`

`\bold{\left(-1\right)^(19)}`

Apply Exponent Rule
`\bold{\left(-a\right)^n=-a^n,\:\mathrm{if\:}n\mathrm{\:is\:odd}}`

`\bold{\left(-1\right)^(19)=-1^(19)}`

`\bold{-1^(19)}`

Solve
`\bold{1^(19)=1}`

`\bold{-1}`

Regards,

Mordancy

Answer 2

it simplifies to -1 :)