Is this even possible?

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Is this even possible?

[math]\sqrt{6} = \sqrt{9-3} = 3+i\sqrt{3}[/math]

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Are you implying that [math]\sqrt{x}+\sqrt{y}=\sqrt{x+y}[/math]?

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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, [math]16=\sqrt{256}=\sqrt{64+64+64+64} \neq \sqrt{64}+\sqrt{64}+\sqrt{64}+\sqrt{64}=8*4=32[/math]

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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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Test:

[math]2 + 2 = topkek[[/math]

Test: [math]2 + 2 = topkek[[/math]

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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 [math]r[/math] can be written as [math]r + 0i[/math].

Assume it can also be written as [math]a + bi[/math], with [math]a , b[/math] real and [math]b \neq 0[/math].

Then, [math]r + 0i = a + bi[/math] implies [math]\frac{r-a}{b} = i[/math]. 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?

[math] z e^{ i\alpha } = z \cos \alpha + i\sin \alpha [/math]?

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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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>>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 [math] 0.5 + 0.i [/math] 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.

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