\[ \Re(z)=3,\qquad \Im(z)=-2 \]

\[ (2+3i)+(1-5i)=3-2i \]

\[ \boxed{3-2i} \]

\[ (4+i)-(2-3i)=4+i-2+3i=2+4i \]

\[ \boxed{2+4i} \]

\[ (1+i)(2+3i)=2+3i+2i+3i^2 \] \[ =2+5i-3=-1+5i \]

\[ \boxed{-1+5i} \]

\[ i^2+i^2=-1-1=-2 \]

\[ \boxed{-2} \]

\[ \overline z=4+7i \]

\[ \boxed{4+7i} \]

\[ z\overline z=3^2+4^2=9+16=25 \]

\[ \boxed{25} \]

\[ |z|=\sqrt{3^2+4^2}=\sqrt{25}=5 \]

\[ \boxed{5} \]

Le point associé est : \[ M(2;-5) \]

\[ \boxed{M(2;-5)} \]

Oui, car : \[ 6=6+0i \]

\[ \boxed{\text{Oui}} \]

\[ |1+i|=\sqrt{1^2+1^2}=\sqrt{2} \]

\[ \boxed{\sqrt{2}} \]

(a) \[ \Re(z)=2,\qquad \Im(z)=3 \]

(b) \[ \overline z=2-3i \]

(c) \[ |z|=\sqrt{2^2+3^2}=\sqrt{13} \]

\[ \boxed{\Re(z)=2,\ \Im(z)=3,\ \overline z=2-3i,\ |z|=\sqrt{13}} \]