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tresset_1 [31]
2 years ago
11

Simplify i^82 pls...thanks :)

Mathematics
2 answers:
Fofino [41]2 years ago
8 0
To simplify i^82, divide 82 by. the answer is 20 with remainder 2
Kruka [31]2 years ago
8 0

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.

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