On 3/8/2025 11:39 PM, Richard Hachel wrote:
Resolve x^4=-1296
x ∈ {
6⋅cos(45°)+6𝑖⋅sin(45°),
6⋅cos(135°)+6𝑖⋅sin(135°),
6⋅cos(225°)+6𝑖⋅sin(225°),
6⋅cos(315°)+6𝑖⋅sin(315°)}
Resolve x^6=-64
x ∈ {
2⋅cos(30°)+2𝑖⋅sin(30°),
2⋅cos(90°)+2𝑖⋅sin(90°),
2⋅cos(150°)+2𝑖⋅sin(150°),
2⋅cos(210°)+2𝑖⋅sin(210°),
2⋅cos(270°)+2𝑖⋅sin(270°),
2⋅cos(330°)+2𝑖⋅sin(330°)}
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Public Service Announcement.
𝑖² = -1 means
never looking up trigonometric formulas.
⎛ cos(a+b)+𝑖⋅sin(a+b) =
⎜
⎜ 𝑒⁽ᵃ⁺ᵇ⁾ⁱ = 𝑒ᵃⁱ⋅𝑒ᵇⁱ =
⎜
⎜ (cos(a)+𝑖⋅sin(a))⋅(cos(b)+𝑖⋅sin(b)) =
⎜
⎜ (cos(a)cos(b)-sin(a)sin(b))+
⎝ 𝑖⋅(sin(a)cos(b)+cos(a)sin(b))
cos(a+b) = cos(a)cos(b)-sin(a)sin(b)
sin(a+b) = sin(a)cos(b)+cos(a)sin(b)
etc.
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