Question

[Nguyễn Thùy Trang]

Bài 3. Cho số phức z = a + bi \(a,b ∈ R)z=a+bi(a,b ∈ R) thoả mãn 

Giá trị biểu thức a2 + b2 - ab bằng:

giúp mik vs

A. 0

B. 1

C. 29/100

D. 5S

Answer 1

[Đoàn Đức Hà]

\(\frac{2-iz}{2+i}-\frac{z+2i}{1-2i}=2\overline{z}\)

\(\Leftrightarrow\frac{2-i\left(a+bi\right)}{2+i}-\frac{a+bi+2i}{1-2i}=2\left(a-bi\right)\)

\(\Leftrightarrow\frac{\left(b+2-ai\right)\left(2-i\right)}{\left(2+i\right)\left(2-i\right)}-\frac{\left[a+\left(b+2\right)i\right]\left(1+2i\right)}{1-2i}=2\left(a-bi\right)\)

\(\Leftrightarrow\frac{2\left(b+2\right)-a-\left(2a+b+2\right)i}{5}-\frac{a-2b-4+\left(2a+b+2\right)i}{5}=2\left(a-bi\right)\)

\(\Leftrightarrow\left[\left(2b+4\right)-a-\left(a-2b-4\right)-10a\right]-\left(2a+b+2+2a+b+2-10b\right)i=0\)

\(\Leftrightarrow\hept{\begin{cases}-12a+4b=-8\\4a-8b=-4\end{cases}}\Leftrightarrow a=b=1\).

\(a^2+b^2-ab=1^2+1^2-1.1=1\)