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OpenStudy (anonymous):
\[\sqrt[3]{-1}\]
OpenStudy (anonymous):
wow
OpenStudy (anonymous):
how much is -1*-1
OpenStudy (anonymous):
\[-1*-1\]
OpenStudy (anonymous):
When I do this on my calculator, the answer says its \[\frac{ 1 }{2 }+\frac{ \sqrt{3} }{ 2}*i\]
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OpenStudy (anonymous):
I don't understand how this is possible...
OpenStudy (anonymous):
dude answer is -1!!
OpenStudy (anonymous):
u got that??
OpenStudy (anonymous):
-1x-1x-1
OpenStudy (anonymous):
yes...
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OpenStudy (anonymous):
so next part
OpenStudy (anonymous):
what u see there is complex number
OpenStudy (anonymous):
under complex number.....which u will learn later.............i=\[-1^{(1/2)}\]
OpenStudy (anonymous):
I already learned complex numbers
OpenStudy (anonymous):
using complex numbers we equate negative square roots which aren't defined under real numbers......
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OpenStudy (anonymous):
oh
OpenStudy (anonymous):
in that case turn the equation into i form
OpenStudy (anonymous):
what do u get??
OpenStudy (anonymous):
\[like~i^{2}=-1\]
OpenStudy (anonymous):
I also tried this on the calcultor and got \[(\frac{ 1 }{ 2 }+\frac{ \sqrt{3} }{ 2 }*i)^{3}=-1\]
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OpenStudy (anonymous):
it is correct
OpenStudy (anonymous):
i still don't get this
OpenStudy (anonymous):
then u have to use the exponential notation
OpenStudy (anonymous):
of complex numbers
OpenStudy (anonymous):
it is of the form a+iB
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OpenStudy (solomonzelman):
you can remember that: \(\Large\color{teal}{ \sqrt[\LARGE \rm odd~number]{-1} =-1 }\).
OpenStudy (solomonzelman):
talking about an integer odd number of course
OpenStudy (anonymous):
@SolomonZelman I think he wants to know how the calculator got that answer
OpenStudy (solomonzelman):
commn
OpenStudy (anonymous):
A+iB>>> A=1/2 and B=\[3^{1/2}/2\]
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OpenStudy (anonymous):
getting it.......??? If u know Complex numbers u will understand me
OpenStudy (anonymous):
i honestly don't know how to do that in a calculator my teacher teaches us without calcs so we do this by hand it just like \[\left( \sqrt{-1} \right)^{\frac{ 3 }{ 1 }}\] which would look like \[\left( \sqrt[3]{-1} \right)^{1}\] i think. I might have the first equation exponent backwards