In this lesson we're going to give some definitions to complete our introduction to the set of Complex Numbers and then we'll solve some exercises as a training to next classwork.
Some definitions and properties.
Complex conjugate: given a complex number z=a+ib, the number a-ib is called its coonjugate and denoted by: .
Real part: given a complex number z=a+ib, the number a is called its real part and denoted by Re(z).
Imaginary part: given a complex number z=a+ib, the number b is called its imaginary part and denoted by Im(z).
Argument: given a complex number z=a+ib=[ρ,θ], the number θ is called its argument and denoted by arg(z).
Absolute value: given a complex number z=a+ib=[ρ,θ], the number ρ is called its absoulte value, or modulus, and denoted by |z|, as with real numbers.
For every complex number z we have Re(z) = (z + )/2 and Im(z) = (z - )/2.
For every complex number z we have .
Final exercises
Downlaod the exercises (pdf file).
This is the last lesson of our short introduction to the set of Complex Numbers. As a training to the classwork you can use all the sheets of exercises given so far and try to solve by yourselves the exercises used as examples during classes.