\(\left(\dfrac{1+i}{1-i}\right)^{10}+2\left(\dfrac{1+i}{1-i}\right)^3\) bằng
\(-1-2i\).\(1+2i\).\(1-2i\).\(-1+2i\).Hướng dẫn giải:\(\left(\dfrac{1+i}{1-i}\right)^{10}+2\left(\dfrac{1+i}{1-i}\right)^3=\left[\dfrac{\left(1+i\right)^2}{\left(1-i\right)\left(1+i\right)}\right]^{10}+2\left[\dfrac{\left(1+i\right)^2}{\left(1-i\right)\left(1+i\right)}\right]^3\)
\(=\left[\dfrac{1+2i+i^2}{2}\right]^{10}+2\left[\dfrac{1+2i+i^2}{2}\right]^3\)
\(=\left(\dfrac{2i}{2}\right)^{10}+2\left(\dfrac{2i}{2}\right)^3\)
\(=i^{10}+2i^3\)
\(=-1-2i.\)