What about plain old x = -10?
-10 ^ 2 = 100
-10 ^ 3 = -1000
-10 ^ 5 = -100000
What about plain old x = -10?
-10 ^ 2 = 100
-10 ^ 3 = -1000
-10 ^ 5 = -100000
When all you have is an imaginary hammer, everything looks like a rotation around the imaginary unit circle.
Explanation of maths
x = -10, i = √-1 so i² = -1 and 10i²=-10
Found the math but no explanation.
The squareroot of 100 is ±10.
The square root is always positive, but you can plug it into the quadratic formula to get the two possible values.
Okay, fine the square roots of 100 are ±10.
There's no reason to bring the quadratic formula into this. Square roots can be negative, but when talking about the square root it's normally assumed to be the principal square root, which is the positive one.
Nope. To clarify, square roots are the opposite of squaring.
Now ask yourself:
What is 10² ?
What is (-10)² ?
If you get the same answer, then they are both the roots of the answer. +10 and -10 then gets together called ±10
IIRC, your spoilery “so” is the other way round. The right side is the definition, and the left-hand side a layman’s shorthand, as the root operator isn’t defined on negative numbers.
I might very well be wrong. My being a mathematician has been over for a while now, my being a pedantic PITA not though.
Wait, isn’t x just -10 if x^3 is not 1000?
My brain
It hurts
That's because the explanation was about 10 times as complicated as it needs to be
What an extremely unnecessary explanation. As a math teacher I would have deducted points for this answer.
No definition what values are suitable for x.
x has to be -10, right? Or am I missing something?
Yeah, I think the point is that the person answering was wrong/over complicating. If x=10i, then x^2 would be -100 (or potentially -10 depending on what you think the ^2 is applied to).
Depends on what are the allowed values for x are. Real numbers, complexe numbers, binary or I made up my own numbers ;)
Probably what they were going for, but there are literally an infinite number of exotic arithmetic spaces you could ask this question in. For example, x=10 works in any ring with a modulus greater than 100 and less than 1000.
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