We equip the complex plane with a direct orthonormal coordinate system ( $\mathrm { O } ; \vec { u } , \vec { v }$ ). For each of the three following propositions, indicate whether it is true or false and justify the chosen answer. One point is awarded for each correct answer properly justified. An unjustified answer is not taken into account. Proposition 1 The set of points in the plane with affixe $z$ such that $| z - 4 | = | z + 2 \mathrm { i } |$ is a line that passes through the point A with affixe 3i. Proposition 2 Let ( $E$ ) be the equation $( z - 1 ) \left( z ^ { 2 } - 8 z + 25 \right) = 0$ where $z$ belongs to the set $\mathbb { C }$ of complex numbers. The points in the plane whose affixes are the solutions in $\mathbb { C }$ of the equation ( $E$ ) are the vertices of a right triangle. Proposition 3 $\frac { \pi } { 3 }$ is an argument of the complex number $( - \sqrt { 3 } + \mathrm { i } ) ^ { 8 }$.
We equip the complex plane with a direct orthonormal coordinate system ( $\mathrm { O } ; \vec { u } , \vec { v }$ ).
For each of the three following propositions, indicate whether it is true or false and justify the chosen answer.\\
One point is awarded for each correct answer properly justified. An unjustified answer is not taken into account.
\textbf{Proposition 1}\\
The set of points in the plane with affixe $z$ such that $| z - 4 | = | z + 2 \mathrm { i } |$ is a line that passes through the point A with affixe 3i.
\textbf{Proposition 2}\\
Let ( $E$ ) be the equation $( z - 1 ) \left( z ^ { 2 } - 8 z + 25 \right) = 0$ where $z$ belongs to the set $\mathbb { C }$ of complex numbers. The points in the plane whose affixes are the solutions in $\mathbb { C }$ of the equation ( $E$ ) are the vertices of a right triangle.
\textbf{Proposition 3}\\
$\frac { \pi } { 3 }$ is an argument of the complex number $( - \sqrt { 3 } + \mathrm { i } ) ^ { 8 }$.