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If w = cos theta + sin theta
Find the modulus and argument of (1-w^2)*
I was asked the above question by a student - it's an IB Higher Level maths question - there is an alternative method which is fine, but Method 1 in the markscheme has a bit which states:
arg((1-w^2)*) = alpha therefore tan alpha = cot theta
(where w = cos theta + sin theta
* is the complex conjugate
arg is the argument)
How is this relationship between tan alpha and cot theta derived? It's only stated in the markscheme, which implies it is obvious - possibly derived from a formula. But I can't find anything anywhere which would lead to this being an obvious relationship.
Any ideas?
Thanks! :)
If w = cos theta + sin theta
Find the modulus and argument of (1-w^2)*
I was asked the above question by a student - it's an IB Higher Level maths question - there is an alternative method which is fine, but Method 1 in the markscheme has a bit which states:
arg((1-w^2)*) = alpha therefore tan alpha = cot theta
(where w = cos theta + sin theta
* is the complex conjugate
arg is the argument)
How is this relationship between tan alpha and cot theta derived? It's only stated in the markscheme, which implies it is obvious - possibly derived from a formula. But I can't find anything anywhere which would lead to this being an obvious relationship.
Any ideas?
Thanks! :)
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