Mathematics
6 Online
OpenStudy (gahm8684):
Imaginary complex numbers
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OpenStudy (zzr0ck3r):
THEY ARE EVERYWHERE!!!!!
OpenStudy (gahm8684):
I've been asked to solve this equation, however when I get to certain step I get stuck and don't know what to do \[x^2+2x+3=0\]
OpenStudy (zzr0ck3r):
What step?
OpenStudy (gahm8684):
\[(-2\pm \sqrt{4-12})/2\]
OpenStudy (gahm8684):
my bad I meant \[-2\pm \sqrt{-8}/2\]
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OpenStudy (zzr0ck3r):
\[\sqrt{4-12}=\sqrt{-8}=\sqrt{-1*8}=\sqrt{-1}\sqrt{8}=i\sqrt{8}=i\sqrt{4*2}=i\sqrt{4}\sqrt{2}=2i\sqrt{2}\]
OpenStudy (gahm8684):
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooohohohhohhohoohohohohohohohoohohohohohhhhhhhhhhhhhhhh
OpenStudy (zzr0ck3r):
Yoou should end up with \(-1\pm i\sqrt{2}\)
OpenStudy (gahm8684):
I get it.
OpenStudy (zzr0ck3r):
word
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OpenStudy (gahm8684):
Thank you
OpenStudy (zzr0ck3r):
np
OpenStudy (gahm8684):
How did you get the -1 tho
OpenStudy (zzr0ck3r):
\(-8=-1*8\)
OpenStudy (gahm8684):
no, I'm talking about the one in -1pmisqrt(2)
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OpenStudy (zzr0ck3r):
\(\dfrac{-2\pm2i\sqrt{2}}{2}=\dfrac{-2}{2}\pm \dfrac{2i\sqrt{2}}{2}=-1\pm i\sqrt{2}\)
OpenStudy (gahm8684):
what about the 2i, what happened to the 2?
OpenStudy (zzr0ck3r):
\[\dfrac{-2}{2}\pm\dfrac{2i\sqrt{2}}{2}=\dfrac{\cancel{-2}}{\cancel{2}}\pm\dfrac{\cancel{2}i\sqrt{2}}{\cancel{2}}=-1\pm i\sqrt{2}\]
OpenStudy (zzr0ck3r):
\[\dfrac{ab+cb}{b}=a+c\]
OpenStudy (gahm8684):
alright I get it now thank you
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OpenStudy (zzr0ck3r):
np