Question

Simplify.

i^68

A. -i

B. 1 (I think it's B, please tell me if it's right or not. Thank you.)

C. -1

D. i

Answer 1

B. 1

Explanation:

Isolate i on one side of the equation.

First, use exponent rule.

`\displaystyle \mathsf{A^B^C=(A^B)^C}}`

`\displaystyle \mathsf{(I^2)^3^4=I^6^8}}`

`\displaystyle \mathsf{(I^2)^3^4}}`

Solve. (by imaginary number rule.)

i²=-1

(-1)³⁴

=1³⁴

1³⁴=1

=1

`\Large\boxed{\mathsf{\Rightarrow 1}}}`

In conclusion, the final answer is (B.) 1.