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OpenStudy (walters):
show the following .pls
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OpenStudy (walters):
Re\[ \left\{ \sin ^{-1} \right\}=\frac{ 1 }{ 2 }\left\{ \sqrt{x ^{2}+y ^{2}+2x+1} \\-\sqrt{x ^{2}+y ^{2}-2x+1}\right\}\]
OpenStudy (primeralph):
Question not complete.
OpenStudy (walters):
it is \[\sin ^{-1}z\]
OpenStudy (jdoe0001):
\(\bf \large sin ^{-1}(\square?) =\cfrac{ 1 }{ 2 } \pm\sqrt{x^2+y^2+2x+1} \ \ ?\)
OpenStudy (primeralph):
Where did y come from?
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OpenStudy (walters):
i think z is complex
OpenStudy (walters):
then \[z=x+yi\]
OpenStudy (walters):
don't forget that Re is real in complex
OpenStudy (walters):
@phi
OpenStudy (primeralph):
@walters Can you post the problem from scratch and everything that has to do with it?
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OpenStudy (walters):
ok give a minute
OpenStudy (walters):
Show that Re\[ \left\{ \sin ^{-1} z\right\}=\frac{ 1 }{ 2 }\left\{ \sqrt{x ^{2}+y ^{2}+2x+1}\\-\sqrt{x ^{2}+y ^{2}-2x+1} \right\}\]
OpenStudy (walters):
this is hoe the question is so since i am working with complex numbers i think \[z=x+yi\]
OpenStudy (primeralph):
I don't think that is correct. The solution contains some natural logs.
Are you sure z = x + yi?
OpenStudy (walters):
i am not sure this is i was thinking since we are in complex numbers
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OpenStudy (walters):
so wat is?
OpenStudy (primeralph):
It's really ugly if z = x+yi. Very long.
OpenStudy (walters):
so do u have any idea how to do it
OpenStudy (primeralph):
It all depends on what z equals.
OpenStudy (walters):
can u show me how long can it be?
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OpenStudy (primeralph):
Wait, just the real part?
OpenStudy (primeralph):
Yes, it is correct.
OpenStudy (walters):
so can u help
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