Imaginary Number
The "unit" Imaginary Number- the equivalent of 1 for Real Numbers- is √(-1) (a negative square root)
In order to figure out the value of to a certain power, one must memorize the following pattern:
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| ***The pattern begins at the top, and continues to the right*** |
This cycle will repeat every four numbers, so if the exponent is a multiple of 4, then the answer is 1.
EXAMPLE # 1:
| i^8 | ||
| Since, 8 is a multiple of 4 you can just use the pattern therefore, the answer is 1. EXAMPLE # 2: i^7= A way to think of this is: 4 goes into 7 one time-if you subtract 4 from 7 the answer is 3. Therefore you should counting three times after 4. i^1= i i^2= -1 i^3= -i i^4= 1 *As you can see, the pattern is starting over, and since you got 3 left over you have to count after, i to the fourth power. i^5= i i^6= -1 i^7= -i | ||
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