Question

Simplify:i^45+i^46 +i^42 - i^35
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Answer 1

Explanation:

i^45 + i^46 + i^42 - i^35

We know that i^4 = 1, so we can simplify some of the exponents:

i^45 = i^(411 + 1) = i^1 = i

i^46 = i^(411 + 2) = i^2 = -1

i^42 = i^(410 + 2) = i^2 = -1

i^35 = i^(48 + 3) = i^3 = -i

So we have:

i + (-1) + (-1) - (-i)

Now we can simplify further by combining like terms:

i - 1 - 1 + i = i - 2 = -1 + i

So the simplified expression is -1 + i.