Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Complex numbers and their geometrical properties

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Original post by Itsmikeysfault

I solved it both ways. Using trig was faster and required less thinking. Most further maths students would agree

I was simply curious about how you solved it.

Original post by mqb2766

I was simply curious about how you solved it.

Oh okay. Here's my working out
2021_11_26 17_26 Office Lens (2).jpg

2021_11_26 17_26 Office Lens (2).jpg

Original post by Itsmikeysfault

Oh okay. Here's my working out
2021_11_26 17_26 Office Lens (2).jpg

2021_11_26 17_26 Office Lens (2).jpg

Its not too bad. When you get the geometric series (sum) its basically
(1 - e^(i8x))/(1 - e^(i2x))
factoring e^i4x out of the numerator and e^ix out of the denominator (both unity magnitude), youre left with
|e^(-i4x) - e^(i4x)| / |e^(-ix) - e^(ix)| = sin(4x)/sin(x)

Theres not a great deal in it either way (when they're both are done properly).

(edited 2 years ago)

only legends use complex numbers

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