sorry Guys but my math teachers gave 30 problems For us he thinks that i don't have only Math to do it , i don't have a lot of times i'll wake up today to study lol.
anyway i stopped in 3 question - Hard For me
z is a complex number, prove if
{1 - iz
-------} = 1, then z is real
1 + iz
my second question:
that is to say A and B are two points of the plan of respective affixes zA, zB
will
a.Prove that [zA-ZB] = AB
B. find all the numbers complexes z such as the triangle whose tops are the images of 1, Z, z^2 is equilateral
and my last question:
Z and z' are two complex numbers unspecified.
Show that [z+z'] ^2 + {z-z'] ^2 = 2 {[Z} 2 + {z'} ^2}
P.s: i don't know how to write them so [ ] =
Many Thanks Guys
1). I think it's about .
Then . (1)
Let .
Then the equality (1) becomes .
Square both sides: .
So, .
2)
a) Let
Then .
.
b) Let
Then ABC is equilateral (2)
The equalities (2) can be written as .
Suppose that , otherwise the triangle degenerates to a point. Then , so we can divide all three members by .
We get
.
Let .
Then .
Solving the system, we get .
3) We'll use the relation .