SOLUTION: May I have some help finishing this expression? Evaluate the expression and write the result in the form a + bi. i^402

Question 120459: May I have some help finishing this expression?
Evaluate the expression and write the result in the form a + bi.
i^402
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First take the exponent 402 and divide by 4.
When it leaves a remainder of 0, the answer is .
When it leaves a remainder of 1, the answer is .
When it leaves a remainder of 2, the answer is .
When it leaves a remainder of 3, the answer is .

Since leaves a remainder of 2, this means the answer is .

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Answer:

So which looks like in form
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
i=sqrt(-1)
i^2=-1
i^3=-sqrt(-1)
i^4=1
The above sequence keeps infinitely repeating as the exponents increase.
So, 402/4 has a remainder of 2 and is the same as i^3 or -sqrt(-1) or -i.
.
Ed
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