Question

Sa se rezolve in C ecuatia

|z|-iz=1-2i

Answer 1

$\sqrt{a^{2}+b^{2} }$-i(a+bi)=1-2i
$\sqrt{a^{2}+b^{2} }$-ai-bi²-1+2i=0
$\sqrt{a^{2}+b^{2} }$-ai+b-1+2i=0
($\sqrt{a^{2}+b^{2} }$+b-1)+i(-a+2)=0
egalezi fiecare paranteza cu 0.
-a+2=0⇒a=2  - il inlocuiesti pe a cu 2 in cealalta relatie
$\sqrt{a^{2}+b^{2} }$-b+1=0
$\sqrt{2^{2}+b^{2} }$-b+1=0
$\sqrt{4+b^{2} }$=b-1   |²
4+b²=(b-1)²
4+b²=b²-2b+1
4=-2b+1
3=-2b
-3=2b⇒b=$\frac{-3}{2}$.

z=2-$\frac{3}{2}$ i