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Using your knowledge of complex numbers, such as De Moivre's and Euler's formulae, verify the trigonometric identities for the double angle.

de Moivre's: (cos(x)+isin(x)) n =cos(nx)+isin(nx) set n=2 (cos(x)+isin(x)) 2 =cos 2 (x)+2isin(x)cos(x)-sin 2 (x), which, according to de Moivre's cos 2 (x)+2isin(x)cos(x)-sin 2 (x)=cos(2x)+isin(2x) We notice...
CP
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What is the mathematical relationship between the frequencies of musical notes that we perceive identical, but at different octaves?

Humans have a logarithmic perception of the majority of uncountable and some countable things. A 0 , which is percieved as the basic note, has a frequency of 27.50 Hz. A 1 =55 Hz, and A 2 =110 Hz. You might ...
CP
Answered by Cezar P. • Physics tutor
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Discuss the role of women in Hamlet.

Despite it being frequently argued that the women in Hamlet are “drawn in fainter lines than their male counterparts,” it appears that upon closer inspection their roles are much more integral to the play an...
IA
12265 Views

Please explain why you are applying to your course, and how you might demonstrate that in 4000 characters.

This question really makes you think about why you are applying to the course that you have chosen. This seems like an obvious statement, but you'd be surprised at just how difficult it might be. Actually st...
SK
4879 Views

How should I begin to analyse an unseen poem?

Firstly, read the question carefully, highlighting any key words i.e 'power' or 'nature' if it is thematic or ' structure' or 'metaphor' if it is technical, to keep in mind when reading the poem. Keeping the...
IF
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