Complex Numbers

Question 1

What is z and z*? And what is their relation?

Answer 1

Z= x + yi and z*= x -yi

If z is a root so is z*

Question 2

What is the other forms of z?

Answer 2

Z= r( cosx + isinx) and z=re^ix

Question 3

What does the question
(z-x+yi)=(z-a+bi) represent?

Answer 3

Perp bisector

Question 4

What are half lines in the form of?

Answer 4

Arg( z-z1) = x

Question 5

What is de moiveres theorem?

Answer 5

R(cosx + sinx)^n = r^n(cosnx + isinnx)
Where you correspond the real and imaginary parts

Question 6

What is the nth root of complex numbers?

Answer 6

W^k = cos(2kpi/n) + isin(2kpi/n) where z^n= a and k starts at 0 all the way to n-1

W^k= p^1/n ( cos( @+2kpi/n) + isin(@+2kpi/n) ) where z^n= x + yi and @ is the principial argument and p is the modulus of x+yi