The question: such that w is a complex number I tried using the identity to get a solution, but it appears to create a mess. :/ Any assistance would be great.
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. Now try to solve for ...
Originally Posted by Prove It . Now try to solve for ... I'm not sure this will work since , not a^2, when a is complex. @OP: I'd be inclined to substitute w = x + iy and take it from there, messy as it's likely to be .... (Where has the question come from?)
Originally Posted by mr fantastic I'm not sure this will work since , not a^2, when a is complex. @OP: I'd be inclined to substitute w = x + iy and take it from there, messy as it's likely to be .... (Where has the question come from?) It's part of a complex analysis question: Show that the function f defined by maps the unit circle onto the interval [-2, 2]
Originally Posted by Glitch It's part of a complex analysis question: Show that the function f defined by maps the unit circle onto the interval [-2, 2] If is on the unit circle then , so . Then So...
Last edited by awkward; Mar 19th 2011 at 01:46 PM. Reason: typo
Originally Posted by awkward If is on the unit circle then , so . Sorry, I'm not sure how you came to the conclusion that .
Because on the unit circle, .
Oh, right. >_< I need stronger coffee.
Originally Posted by awkward OK, so I've worked out what you've done so far. This is what I've done: Let z = x + iy So unless I'm mistaken, this is a parabola. I'm fairly sure this isn't the correct solution. :/
Originally Posted by Glitch OK, so I've worked out what you've done so far. This is what I've done: Let z = x + iy So unless I'm mistaken, this is a parabola. I'm fairly sure this isn't the correct solution. :/ Since (x,y) is on the unit circle, . So then what is the range of ?
Ahh, thanks.
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