Question

NUMERE COMPLEXE
Macar un subpunct
NU ȘTII NU RĂSPUNDE DAU REPORT!!!​

Answer 1

$\it a) \ \ z=2a-1+(a+1)i \\ \\ Re(z)\cdot Im(z)=2 \Rightarrow (2a-1)(a+1)=2 \Rightarrow 2a^2+2a-a-1-2=0 \Rightarrow \\ \\ \Rightarrow 2a^2+a-3=0 \Rightarrow 2a^2+3a-2a-3=0 \Rightarrow a(2a+3)-(2a+3)=0 \Rightarrow \\ \\ \Rightarrow (2a+3)(a-1)=0 \Rightarrow \begin{cases} \it 2a+3=0 \Rightarrow a_1=-\dfrac{3}{2}\\ \\ \it a-1=0\ \Rightarrow \ \ a_2=1\end{cases}$

$\it b)\ z=m^2+m+2i\\ \\ Re(z)+Im(z)=4 \Rightarrow m^2+m+2=4|_{-4} \Rightarrow m^2+m-2=0 \Rightarrow \\ \\ \Rightarrow \ m^2+2m-m-2=0 \Rightarrow\ m(m+2)-(m+2)=0 \Rightarrow\\ \\ \Rightarrow (m+2)(m-1)=0 \Rightarrow \begin{cases} \it m+2=0 \Rightarrow m_1=-2\\ \\ \it m-1=0 \ \Rightarrow \ m_2=1\end{cases}$