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Câu hỏi: Cho số phức $z=1-\dfrac{1}{3}i$. Tìm số phức $\text{w}=i\overline{z}+3z$.
A. $\text{w}=\dfrac{8}{3}$.
B. $\text{w}=\dfrac{8}{3}+i$.
C. $\text{w}=\dfrac{10}{3}$.
D. $\text{w}=\dfrac{10}{3}+i$.
A. $\text{w}=\dfrac{8}{3}$.
B. $\text{w}=\dfrac{8}{3}+i$.
C. $\text{w}=\dfrac{10}{3}$.
D. $\text{w}=\dfrac{10}{3}+i$.
Ta có $z=1-\dfrac{1}{3}i\Rightarrow \overline{z}=1+\dfrac{1}{3}i$
Khi đó: $\text{w}=i\overline{z}+3z=i(1+\dfrac{1}{3}i)+3(1-\dfrac{1}{3}i)=\dfrac{8}{3}$
Khi đó: $\text{w}=i\overline{z}+3z=i(1+\dfrac{1}{3}i)+3(1-\dfrac{1}{3}i)=\dfrac{8}{3}$
Đáp án A.