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Jan
26
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Jan
7
comment Why $\sqrt{-1 \times {-1}} \neq \sqrt{-1}^2$?
@JohannesHahn: What you describe is what I'm calling the domain of the identity and I'm not making that terminology up myself. I've seen it used in several texts.
Dec
23
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23
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Nov
15
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Oct
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19
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Aug
2
revised How many ways are there to define sine and cosine?
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Jul
22
comment Penrose Tile generator
Being able to fill a rectangular region is different from creating a tileable rectangle (a rectangle for which opposite edges can be glued together to continue the pattern seamlessly).
Jul
20
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Jul
15
comment How to find shortest distance between two skew lines in 3D?
If $D_1=D_2$, the lines aren't skew.
Jul
11
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2
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30
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27
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May
12
revised Area of a triangle from some of its parts
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Apr
28
comment Why $\sqrt{-1 \times {-1}} \neq \sqrt{-1}^2$?
@SufyanNaeem: No. First off, $b\neq 0$ since we're dividing by $b$. Beyond that, your example "since..." is not true because of the broad rule $\sqrt{ab}=\sqrt{a}\sqrt{b}$, but because of the narrower rule $\sqrt{-a}=i\sqrt{a}$ for $a>0$. In particular, take another look at the paragraph beginning "In general..." in my answer.
Apr
10
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Apr
2
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