# User:Adam majewski

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Some notes from | wikipedia

$Z^2$ $Real = x^2 - y^2$ $Imag = 2 * x * y$

$Z^3$ $Real = x^3 - 3* y^2 * x$ $Imag = 3 * x^2 * y - y^3$

$Z^4$ $Real = x^4 - 6 * x^2 * y^2 + y^4$ $Imag = 4*x^3 * y - 4 * x * y^3$

$Z^5$ $Real = x^5 - 10 * x^3 * y^2 + 5 * x * y^4$ $Imag = 5*x^4 * y - 10 * x^2 * y^3 + y^5$

$Z^6$ $Real = x^6 - 15 * x^4 * y^2 +15 * x^2 * y^4 - y^6$ $Imag = 6*x^5 * y - 20 * x^4 * y^2 + 6* x * y^5$

$Z^7$ $Real = x^7 - 21 * x^5 * y^2 + 35 * x^3 * y^4 - 7 * x * y^6$ $Imag = 7*x^6 * y - 35 * x^4 * y^3 + 21* x^2 * y^5 - y^7$,

$Exp(Z)$ $Real = Exp(x) * Cos(y)$   $Imag = Exp(x) * Sin(y)$

$Ln(Z)$ $Real = 0.5 * Ln(x^2 + y^2)$   $Imag = Arctan(y/x)$

$Sin(Z)$ $Real = Sin(x) * ((Exp(y) + Exp(-y))/2)$   $Imag = Cos(x) * ((Exp(y) - Exp(-y))/2)$

$Cos(Z)$ $Real = Cos(x) * ((Exp(y) + Exp(-y))/2)$   $Imag = -Sin(x) * ((Exp(y) - Exp(-y))/2)$

$SinH(Z)$ $Real = Cos(y) * ((Exp(x) - Exp(-x))/2)$   $Imag = Sin(y) * ((Exp(x) + Exp(-x))/2)$

$CosH(Z)$ $Real = Cos(y) * ((Exp(x) + Exp(-x))/2)$   $Imag = Sin(y) * ((Exp(x) - Exp(-x))/2)$

## test

$1 / 237142198758023568227473377297792835283496928595231875152809132048206089502588927 \approx 4.21687917729220928973942962050800760308398455294740302003110521004325771638790385468222014406044810316697454753662... *10^-81$ $\frac{1}{2^{267}-1}= \frac{1}{237142198758023568227473377297792835283496928595231875152809132048206089502588927} \approx 4.216879177292209*10^{-81}$( land on the root point of period 267 component : c267 = 0.250137369683480-0.000003221184145 i with angled internal adress : $1 \xrightarrow{1/267} 267$

( land on the root point of period 268 component c268 = 0.250137369683480-0.000003221184145i period = 10000 i with angled internal adress : $1 \xrightarrow{267/268} 268$

# People

Marius-F. Danca

pl-N Polski jest językiem ojczystym tego użytkownika.
en-2 This user can read and write intermediate English.

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