Mathmatical Studies - Unit 2 > Complex
 
 

Complex Conjugate

If  z=a+ib  then the complex conjugate of z is given by  z*=a-ib.

The complex conjugate has some interesting properties:

z×z*=(a+ib)×(a-ib)=a2+iab-iab-b2i2=a2+b2

I.e. The product of a complex number and its conjugate is a REAL number. This fact is used in division of complex numbers when we 'realise' the denominator.