Cho \({z_1} = 1 + \sqrt 3 i\); \({z_2} = \frac{{7 + i}}{{4 - 3i}}\); \({z_3} = {\left( {1 - i} \right)^{2016}}\). Tìm dạng đại số của \(w = z_1^{25}.z_2^{10}.z_3^{2016}\).
A.\({2^{1037}} - {2^{1037}}\sqrt 3 i.\)
B. \( - {2^{1037}}\sqrt 3 + {2^{1037}}i.\)
C.\( - {2^{1021}}\sqrt 3 + {2^{1021}}i.\)
D.\({2^{1021}}\sqrt 3 - {2^{1021}}i.\)
A.\({2^{1037}} - {2^{1037}}\sqrt 3 i.\)
B. \( - {2^{1037}}\sqrt 3 + {2^{1037}}i.\)
C.\( - {2^{1021}}\sqrt 3 + {2^{1021}}i.\)
D.\({2^{1021}}\sqrt 3 - {2^{1021}}i.\)
\(\left. \begin{array}{l}z_1^{25} = {(1 + \sqrt 3 i)^{25}} = {8^8} + {8^8}\sqrt 3 i\\z_2^{10} = {\left( {\frac{{7 + i}}{{4 - 3i}}} \right)^{10}} = {(2i)^5} = {2^5}i\\z_3^{2016} = {(1 - i)^{2016}} = {( - 2i)^{1008}} = {2^{1008}}\end{array} \right\} \Rightarrow w = z_1^{25}.z_2^{10}.z_3^{2016} = - {2^{1037}}\sqrt 3 + {2^{1037}}i.\)
Vậy chọn đáp án B.
Vậy chọn đáp án B.