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Regneregler - Wordpress starter

Regneregler

1.1.13.2 Regneregler

A±B=(a1±b1)+i(a2±b2) [1.1.226]

AB=(a1b1a2b2)+i(a1b2+a2b1) [1.1.227]

BA=b1+ib2a1+ia2=a1b1+a2b2a12+a22+ia1b2a2b1a12+a22 [1.1.228]

1A=a1a12+a22ia2a12+a22 [1.1.229]

1i=i [1.1.230]

|AB|=|A||B| [1.1.231]

||A||B|||A±B||A|+|B| [1.1.232]

|BA|=|B||A| [1.1.233]

A=|A|(cosargA+isinargA) [1.1.234]

arg(AB)=argA+argB[1.1.235]

argAB=argAargB [1.1.236]

A*±B*=(A±B)* [1.1.237]

A*B*=(AB)* [1.1.238]

B*A*=(BA)* [1.1.239]

A*A=|A|* [1.1.240]

Eulers formler

cosx=12(eix+eix) [1.1.241]

sinx=12(eixeix) [1.1.242]

eix=cosx+isinx [1.1.243]

eix=cosxisinx [1.1.244]

Moivres formel

cosnx+isin nx=(cosx+isinx)n [1.1.245]

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Regneregler, Komplekse tal og funktioner