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Powers of i
| Question: How do we approach problems such as i 1987? |
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Truly answers: When i is raised to a large power such as 1987, we want to use i 4 = 1. This is because i 4 = (i 2)2 = (–1)2 = 1. Begin by dividing the power 1987 by 4. Then,  Therefore, 1987 = 4·496 + 3. We now use some properties of exponents reviewed in Charpter R. i 1987 = i 4·496+3 = (i 4·496)(i 3) = (i 4)496(i 3) = (1)496(i 2·i ) = 1·((–1)·i ) = – i
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Disclaimer • Updated September 4, 2008
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Phone: +1 (610) 462-WPJW