Math Tricks 1

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