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math tricks 1
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Math Formulas:Complex numbersDefinitions:A complex number is written asa+biwhereaandbare real numbers ani, called the imaginary unit, has the property thati2=1.The complex numbersz=a+biandz=abiare called complex conjugate of each other.Formulas:Equality of complex numbersa+bi=c+dia=candb=d
Addition of complex numbers(a+bi)+(c+di)=(a+c)+(b+d)i
Subtraction of complex numbers(a+bi)(c+di)=(ac)+(bd)i
Multiplication of complex numbers(a+bi)(c+di)=(acbd)+(ad+bc)i
Division of complex numbersa+bic+di=a+bic+dicdicdi=ac+bdc2+d2+bcadc2+d2i
Polar form of complex numbersa+bi=r(cos+isin)
Multiplication and division of complex numbers in polar form[r1(cos1+isin1)][r2(cos2+isin2)]=r1r2[cos(1+2)+isin(1+2)]
r1(cos1+isin1)r2(cos2+isin2)=r1r2[cos(12)+isin(12)]
De Moivre's theorem[r(cos+isin)]n=rn(cos(n)+isin(n))
Roots of complex numbers[r(cos+isin)]1/n=r1/n(cos+2kn+isin+2kn)k=0,1,,n1