General Contents
Detailed Contents
Index
Programmed tutorial: Powers of
i
: Example 1
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Simplify i
2
by replacing i by its definition.
Help on
Complex Numbers
General Contents
Detailed Contents
Index
What result do we get for the square of
(the square root of something)?
We get the something.
Apply this to our example.
Note: We'll use this often.
Simplify i
3
by using the previous result and clever factoring.
i
3
= i
2
* i.
Replace i
2
.
We get i
3
= (–1) * i
We don't usually write the (–1). Rewrite this without (–1).
Finally, i
3
= – i.
Simplify i
4
in a similar way (using factors of i
2
).
i
4
= i
2
* i
2
Replace i
2
.
i
4
= i
2
* i
2
= (–1) * (–1) = 1
Summarize these 4 powers.
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