Question

Write the correct letter from column (2) against column (1) :

Answer 1

A) $|z-1(1+2i)|=5$ represent a circle centered at $(1,2)$ and radius $5$
$(x-1)+{(y-2)}^2=25$
B) $\frac{1}{z}=\frac{1}{x+iy}=\frac{x-iy}{x^2+y^2}$
$\Rightarrow Re\left(\frac{1}{z}\right)<\frac{1}{2}\Rightarrow \frac{x}{x^2+y^2}<\frac{1}{2}$
$\Rightarrow 2x<x^2+y^2\Rightarrow x^2+y^2-2x>0\Rightarrow {(x-1)}^2+y^2>1$
Represent exterior a circle centered at $(1,0)$ and radius $1$
C) ${\tan }^{-1}\frac{y}{x-a}=\frac{\pi }{4}\Rightarrow y=(x-a).\tan \frac{\pi }{4}\Rightarrow x-y=a$
Represent a straight line