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2 \times 3
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a_{i-1}
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Comments
For real numbers they are equivalent.
In the complex case, 3i2 usually means the real third root of −1, whereas i32 usually refers to the principal third root of −1 (it has three third roots), which is 21+23i. For instance, you'll get these different values if you enter the expressions in Google or Wolfram Alpha. Enter "cube root of i^2" and you get -1; enter "i^(2/3)" and you get 0.5 + 0.866025404 i. This is purely conventional. (Wolfram helpfully tells you, "Assuming 'cube root' is the real-valued root".)
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
For real numbers they are equivalent. In the complex case, 3i2 usually means the real third root of −1, whereas i32 usually refers to the principal third root of −1 (it has three third roots), which is 21+23i. For instance, you'll get these different values if you enter the expressions in Google or Wolfram Alpha. Enter "cube root of i^2" and you get -1; enter "i^(2/3)" and you get 0.5 + 0.866025404 i. This is purely conventional. (Wolfram helpfully tells you, "Assuming 'cube root' is the real-valued root".)
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Yep but, the domain of third root of x^2 is different from the domain of x^(2/3). How is that possible??
There is no difference in the above expressions
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Yep but, the domain of third root of x^2 is different from the domain of x^(2/3). How is that possible??
There is no difference in the two expressions. But since you are asking then:
3x2=x32
But
x32=(x)2231=(x)2−32
Hope this helps. ⌣
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Yep but, the domain of third root of x^2 is different from the domain of x^(2/3). How is that possible??