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

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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) About Me  (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 1.
When it leaves a remainder of 1, the answer is sqrt%28-1%29=i.
When it leaves a remainder of 2, the answer is -1.
When it leaves a remainder of 3, the answer is -sqrt%28-1%29=-i.


Since 402%2F4 leaves a remainder of 2, this means the answer is -1.

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Answer:

So i%5E402=-1 which looks like -1%2B0i in a+%2B+bi form

Answer by edjones(8007) About Me  (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