Question

Z=(1+i)^9/(1-i)^7 комплексные числа.

Answer 1

Z=(1+i)^9/(1-i)^7

$Z=\frac{(1+i)^9}{(1-i)^7} = \frac{(1+i)^9(1+i)^7}{(1-i)^7(1+i)^7} = \frac{(1+i)^{16}}{(1 - i^2)^7} = \frac{[(1+i)^2]^8}{2^7} = \\ \\ = \frac{(1+2i-1)^8}{2^7} = \frac{2^8i^8}{2^7} =2$