gaokao 2025 Q2

gaokao · China · national-II 5 marks Complex Numbers Arithmetic Complex Division/Multiplication Simplification

Given $z = 1 + \mathrm{i}$, then $\frac{1}{z-1} = $ ( )
A. $-i$
B. $i$
C. $-1$
D. $1$

Given $z = 1 + \mathrm{i}$, then $\frac{1}{z-1} = $ ( )\\
A. $-i$\\
B. $i$\\
C. $-1$\\
D. $1$