1. $z$ is a complex number, then the equation $\left(\frac{1}{5}\right)^{|-3|}=\left(\frac{1}{5}\right)^{|++3|-1}$ represents the graph of
A. a line
B. an ellipse
C. a hyperbola with real semi-axis length 1
D. the right branch of a hyperbola with foci on the $x$-axis and real semi-axis length $\frac{1}{2}$
1. D $\quad|z-3|=|z+3|-1 \quad|z+3|-|z-3|=1$

Translation:
1. D $\quad|z-3|=|z+3|-1 \quad|z+3|-|z-3|=1$