Properties

1. IBMHL Complex Numbers Lesson 5 1
Interesting Properties of Complex Conjugates
1) Show that z+z* and zz* are always real.
2) If z= rcis 𝜃 then z* =
Include a diagram here.
3) If z = x+iy and w = u+iv, prove (z+w)*=z*+w*
4) If z = x+iy and w = u+iv, prove that (zw)* = z*w*
5) If z = x+iy and w = u+iv, prove
!∗
!∗
= (
!
!
)∗

2. IBMHL Complex Numbers Lesson 5 2
6) If z = x+iy, prove (zn)*= (z*)n
Practice:
(i) If z = (1+iw)2 find z*
(ii) Find a complex number such that z = 3z+2z* = 5+2i