For many calculators if you input "the square root of -1", you will get out "domain error"
Input
Output
This was done with a TI-30XS calculator
Why do some calculators give a "domain error" for the square root of a negative?
Complex Numbers
Imaginary NumbersReal Numbers
Rational Numbers Irrational Numbers
Integers
Whole Numbers
Counting Numbers
Because the domain programmed into the calculator is the Real Numbers not the Complex Numbers or Imaginary Numbers
These questions should be on your mind.
2. How do I process them?
1. Why is the square root of a negative useful?
Why is the square root of a negative useful?
Imaginary Numbers are useful in these fields of work:
1. Computer Graphics
2. Electric Engineering
3. Quantum Physics
We can learn about a 4 Cycle System that is a basis of study in these fields.
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i clock
Let's begin with a definition
By definition, "the square root of -1" is named i.
Let's combine that definition with these 2 facts.
Fact #1Any non-zero number to the "zero power" is 1
Fact #2Any number to the "power of 1" is itself
So, the top and the right side of the "i clock" are explained.
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i clock
Let's investigate the bottom position
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i clock
represent?
What does this
But why is this true?
Let's investigate fact #3 first.
Fact #3A "square root" times itself cancels the radical, only
Now the top, right and bottom positions of the clock are explained
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i clock
Let's investigate the position on the left
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i clock
represent?
What does this
But why is this true?
and
A "square root" times itself cancels the radical, only?
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i clock
The "i clock"
What about a power of i that is 4 or greater?
Add to the clock like this.
Let's make sure we understand this
i clock to the 99th power