Take 10 minutes to prepare this exercise.
Then, if you lack ideas to begin, look at the given clue and start searching for the solution.
A detailed solution is then proposed to you.
If you have more questions, feel to ask then on the forum.
Question
1. We denote by
and
two complex numbers with modulus
and we set:
Prove that
is a real number.
2. We denote by
and
two distinct complex numbers of modulus
and by
a complex number.
We set
Prove that
is an imaginary number.
a) Prove that
b) Show that
a)
The complex numbers
and
' having an absolute value of
we have:
et
We infer:
by multiplying the numerator and denominator by
b) Complex number
is purely imaginary if and only if
Complex numbers
and
have an absolute value of
hence
and
which gives:
and by multiplying numerator and denominator by
we get:
