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Câu hỏi: Cho số phức $z$ thỏa mãn $z={{\left( \dfrac{1+i}{1-i} \right)}^{2019}}$. Tính ${{z}^{4}}$.
A. $-1$.
B. $i$.
C. $-i$.
D. $1$.
Ta có $N\left( k;{{\log }_{5}}\left( k+4 \right) \right)$ $=\dfrac{2i}{2}$ $=i$ $\Rightarrow z={{i}^{2019}}$ $\Rightarrow {{z}^{4}}={{\left( {{i}^{2019}} \right)}^{4}}$ $={{\left( {{i}^{4}} \right)}^{2019}}$ $={{1}^{2019}}$ $=1$.
A. $-1$.
B. $i$.
C. $-i$.
D. $1$.
Ta có $N\left( k;{{\log }_{5}}\left( k+4 \right) \right)$ $=\dfrac{2i}{2}$ $=i$ $\Rightarrow z={{i}^{2019}}$ $\Rightarrow {{z}^{4}}={{\left( {{i}^{2019}} \right)}^{4}}$ $={{\left( {{i}^{4}} \right)}^{2019}}$ $={{1}^{2019}}$ $=1$.
Đáp án D.