General Contents
Detailed Contents
Index
Programmed tutorial: Powers of
i
: Example 2
If you find this page helpful and would recommend that I create more pages like this one, please let me know:
Email to John Taylor
If you want to see all of the following steps at once, click the "All Steps" button. Otherwise, use the "Next" button.
Use these results
to obtain simplifications for
i
5
, i
6
, i
7
, and i
8
, by factoring the powers of i.
Help on
Complex Numbers
General Contents
Detailed Contents
Index
First factor i
5
.
i
5
= i
4
* i
Use the above results to replace i
4
.
We get i
5
= (1) * i = i
Now factor i
6
i
6
= i
4
* i
2
Use the above results to replace i
4
.
We get i
6
= (1) * i
2
= i
2
Use the above results again to replace i
2
i
6
= i
2
= –1
Now factor i
7
i
7
= i
4
* i
3
Use the above results to replace i
4
.
We get i
7
= (1) * i
3
= i
3
Use the above results again to replace i
3
i
7
= (1) * i
3
= i
3
= – i
Now factor i
8
i
8
= i
4
* i
4
Use the above results to replace i
4
.
We get i
8
= (1) * (1) = 1
This pattern repeats for each group of 4 powers of i. Use the idea of this pattern to simplify i
17
.
i
17
= i
16
* i, or
i
17
= (i
4
)
4
* i, or
i
17
= (1)
4
* i = i
Simplify i
23
in a similar way.
Here we can group as follows:
i
23
= i
20
* i
3
, or
i
23
= (i
4
)
5
* i
3
, or
i
23
= (1)
5
* i
3
= i
3
In summary, we can always reduce a
power of i to one of the first 4 powers.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
Email to John Taylor
