La 1)
z + 3i = 5z ( z conjugat)
Notam z = a + bi =>
a+bi+3i = 5(a-bi) => a + (3+b)i = 5a - 5bi
Egalam partile reale cu partile imaginare:
=>[tex] \left \{ {{a=5a} \atop {3+b=-5b}} \right. [/tex] [tex]=\ \textgreater \ \left \{ {{a=0} \atop {6b=-3}} \right. =\ \textgreater \ \left \{ {{a=0} \atop {b=- \frac{1}{2}}} \right.=\ \textgreater \ z = 0 - \frac{1}{2}i =\ \textgreater \ z = -\frac{1}{2}i [/tex]
La 2)
|z| = [tex] \sqrt{ a^{2}+ b^{2} } [/tex]
Notezi la fel z= a + bi;
