Show that : i4 + i3 − i2 − 2 = −i.
Question
Show that : i4 + i3 − i2 − 2 = −i.
Solution
Sure, let's break this down:
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First, we need to understand that "i" is the imaginary unit, which is defined as the square root of -1.
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The powers of "i" follow a specific pattern: i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1. After i^4, the pattern repeats.
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So, we can substitute these values into the equation:
i^4 + i^3 - i^2 - 2 = 1 - i - (-1) - 2
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Simplify the equation:
= 1 - i + 1 - 2 = 2 - i - 2 = -i
So, i^4 + i^3 - i^2 - 2 indeed equals -i.
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