A few months ago we introduced the idea of imaginary numbers in ComplexNumber. That concept is found on high school tests, but today's concept is found in both middle school and high school. It showed up twice last year in middle school, with a median placement at question # 75.
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As we discussed in the previous lesson, an imaginary number is the opposite of a real number, and is represented by i, which is √(-1). So i x i = -1. The questions found in middle school are pretty straightforward, but those found on high school tests require a little more calculation.
Let's look at the first several powers of i:
How to Solve:
- Look at the exponent. If it is > 3, subtract the greatest possible multiple of 4 less than the exponent.
- You'll be left with an exponent of 1, 2, 3, or 4. Memorize the pattern above to determine the result.