How do you simplify #i44 + i150 - i74 - i109 + i61#?
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To simplify the expression (i^{44} + i^{150} - i^{74} - i^{109} + i^{61}), we need to consider the powers of (i):
(i^{44}) is equivalent to (i^{4 \times 11}), and since (i^4) equals 1, (i^{44} = 1).
Similarly, (i^{150}) is equivalent to (i^{4 \times 37}), and (i^{4}) equals 1, so (i^{150} = 1).
For (i^{74}), it's equivalent to (i^{4 \times 18 + 2}), and (i^{4 \times 18}) equals 1, while (i^2) equals -1, so (i^{74} = -1).
For (i^{109}), it's equivalent to (i^{4 \times 27 + 1}), and (i^{4 \times 27}) equals 1, while (i^1) equals (i), so (i^{109} = i).
Lastly, (i^{61}) is equivalent to (i^{4 \times 15 + 1}), and (i^{4 \times 15}) equals 1, while (i^1) equals (i), so (i^{61} = i).
Now, substituting these values into the expression:
[1 + 1 - (-1) - i + i] [= 1 + 1 + 1 - i + i] [= 3]
Therefore, the simplified expression is 3.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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