Question

Sa se determine toate numerele complexe z care satisface conditiei: Im z =3, |z-i| = 2

Answer 1

[tex]z=x+iy;y=3 \\ Iz-iI=Ix+3i-iI= Ix+2iI=\sqrt{ x^{2} +4} \\ \sqrt{ x^{2} +4}=2 \\ x^{2} +4=4 \\ x=0 \\ z=3i [/tex]

Answer 2

 z=a+bi
z=Rez+Imz·i
 Im z =3, |z-i| = 2
deci b=3
|z-i|=2
daca z=a+bi =a+3i
|z-i|=|a+3i-i|=|a+2i|
|a+2i|=2
√(a²+4)=2
[√(a²+4)]²=2²
a²+4=4
a²=0
a=0
numarul complex este
z=3i