Mathematics
17 Online
OpenStudy (zenmo):
someone help with an arithmetic for trig.
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OpenStudy (anonymous):
yes.
OpenStudy (zenmo):
\[\sqrt{2}^{7}[(-\sqrt{2}/2)+(-\sqrt{2}/2)i]. How do you get -(\sqrt{2})^{6}-(\sqrt{2})^{6}i\]
OpenStudy (zenmo):
Having a brain fart, so I don't know how you get that answer. :X
OpenStudy (studygurl14):
\(\Large\sqrt{2^7}[\frac{\sqrt{2}}{2}+\frac{-\sqrt{2}}{2}i]\)
like that?
OpenStudy (freckles):
distribute!
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OpenStudy (zenmo):
Yes ^ to studygurl
OpenStudy (studygurl14):
forgot to put the -
OpenStudy (studygurl14):
Okay, so first step it to distribute the \(\large\sqrt{2^7}\) as @freckles said
OpenStudy (freckles):
\[(\sqrt{2})^7 \cdot (\sqrt{2})^1=(\sqrt{2})^8=(\sqrt{2})^6 \cdot (\sqrt{2})^2\]
guess what (sqrt(2))^2=?
OpenStudy (zenmo):
\[its \sqrt{2}^{7}. \sqrt{2} \to the 7th power\]
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OpenStudy (zenmo):
square root of 2 to the 7th power****
OpenStudy (studygurl14):
@freckles is asking what \(\large(\sqrt{2})^2\) equals
OpenStudy (zenmo):
equals to 2?
OpenStudy (studygurl14):
Correct.
OpenStudy (zenmo):
What's next?
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OpenStudy (studygurl14):
you have \(\large\sqrt{2^8}\)
\(\large\sqrt{2^8}\rightarrow\sqrt{2^22^22^22^2}\rightarrow\sqrt{2^2}\sqrt{2^2}\sqrt{2^2}\sqrt{2^2}\rightarrow?\)
OpenStudy (zenmo):
equals to 16*
OpenStudy (studygurl14):
correct
OpenStudy (studygurl14):
Now you have
\(\Large\frac{16}{2}+\frac{-16}{2}i\)
Can you do the rest?
OpenStudy (zenmo):
Yea, I can see the picture now. Thanks!
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OpenStudy (studygurl14):
:)