Question

Simplify i^82 pls...thanks :)

Answer 1

To simplify i^82, divide 82 by. the answer is 20 with remainder 2

Answer 2

Answer:

-1

Step-by-step explanation:

I simplified the expression using the definition of an imaginary number i=√1

First I applied the exponent rule: $a^{bc}=\left(a^b\right)^c$

$i^{82} = \left(i^2\right)^{41}$

$=\left(i^2\right)^{41}$

Then, I applied the maginary number rule: $\:i^2=-1$

$=\left(-1\right)^{41}$

Then I used the exponent rule again: $\left(-a\right)^n=-a^n,\:\mathrm{if\:}n\mathrm{\:is\:odd}$

$\left(-1\right)^{41}=-1^{41}$

$=-1^{41}$

Sooo, $1^{41}=1,$ which equals =-1.