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Is this even possible?
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You are currently reading a thread in /sci/ - Science & Math

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650 B, 188x20
Is this even possible?
$\sqrt{6} = \sqrt{9-3} = 3+i\sqrt{3}$
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Are you implying that $\sqrt{x}+\sqrt{y}=\sqrt{x+y}$?
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>>7812176
wait why doesn't the latex work
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>>7812162
No, you can't break up sums in a radical.

For example, $16=\sqrt{256}=\sqrt{64+64+64+64} \neq \sqrt{64}+\sqrt{64}+\sqrt{64}+\sqrt{64}=8*4=32$
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>>7812187
[eqn] 16 = \sqrt{256} = \sqrt{64+64+64+64} \neq \sqrt{64} + \sqrt{64} + \sqrt{64} + \sqrt{64} = 8 * 4 = 32 [/eqn]

>>7812180
It breaks sometimes for me too.
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You can't split roots unless the inner terms are multiplying or dividing.
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>>7812180
Use spaces in your LaTeX or 4chan will add them for you.
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>>7812190
here
>>7812180
I added spaces in between everything. Also used [eqn] tags but the spaces might have been enough.
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Test:
$2 + 2 = topkek[$

Test: $2 + 2 = topkek[$
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>>7812190
Holy shit I'm really fucking stupid.
Wait so are there any way to write a real number as a complex number with a non-zero immaginary part?
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>>7812202
No.

Because then it wouldn't be a real number dipshit.
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>>7812202
Not really.

A real number $r$ can be written as $r + 0i$.
Assume it can also be written as $a + bi$, with $a , b$ real and $b \neq 0$.
Then, $r + 0i = a + bi$ implies $\frac{r-a}{b} = i$. But this doesn't make any sense, as the left-hand side is a real number while the right side isn't.
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One more question: the modulus of a complex number written in trigonometric form is the same when the complex number is written in imaginary exponential?
$z e^{ i\alpha } = z \cos \alpha + i\sin \alpha$?
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>>7812202
No, that contradicts the definition of a real number.

You sound like you'd be interested in laplace transforms though. They might be a bit above your head but if you're genuinely interested I'd look into it.
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>>7812217
That's Euler's equation.
https://en.wikipedia.org/wiki/Euler%27s_identity
However the z should multiply the entire thing (both the cosine and the sine).
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>>7812223
Sorry this is a better link:
https://en.wikipedia.org/wiki/Euler%27s_formula
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>>7812223
Yeah i forgot the parenthesis. I've never seen euler's formula with a number before $e$ so I assumed it couldn't have a modulus.

>>7812219
Thanks, I know I won't understand everything but I like reading wikipedia article regarding math, just to grasp the concept.
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>>7812202
no because the reals are a subset of the complex.
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>>7812162
Funny how it does make sense if you square both sides and take the real part.
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>>7812202
Top laff
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What does $0.5 + 0.i$ mean?
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>>7812589
It means 0.5.
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>>7812609
And the 0.i? Just a nice way of saying no imaginary part?
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>>7812217
You're missing brackets before cos and ending after alpha, but yeah regardless of how you express a complex number always has the same modulus
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>>7812621
Wherever you found the expression "0.5 + 0.i" was generated by some software that someone wrote and forgot to account for the special case where the imaginary part is exactly 0.

0.i means as much as saying 0.x.