Question

sa se determine nr complexe z
1.z+3i=5z conjugat
2.z+2|z|=13+4i

Answer 1

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:

=>$\left \{ {{a=5a} \atop {3+b=-5b}} \right.$ $=\ \textgreater \ \left \{ {{a=0} \atop {6b=-3}} \right. =\ \textgreater \ \left \{ {{a=0} \atop {b=- \frac{1}{2}}} \right.=\ \textgreater \ z = 0 - \frac{1}{2}i =\ \textgreater \ z = -\frac{1}{2}i$
 
La 2)
|z| = $\sqrt{ a^{2}+ b^{2} }$

Notezi la fel z= a + bi;