Are you familiar with complex circles?

Algebra Level 5

$C_1 \ : \ |z-i|=2$ $C_2 \ : \ |z-1-2i|=4$

Above are two circles in the complex plane. Then ,

C_1 \ and \ C_2

touch each other.

C_2

lies within

C_1

C_1 \ and \ C_2

intersect at two distinct points.

C_1

lies within

C_2

2 solutions

Anandhu Raj
Mar 16, 2016

$C_1 \ : \ |z-i|=2 \Rightarrow { C }_{ 1 }$ is a circle with center $(0,1)$ and radius $2$ units. [ ${ C }_{ 1 }$ is shown Red.]

$C_2 \ : \ |z-1-2i|=4 \Rightarrow { C }_{ 2 }$ is a circle with center $(1,2)$ and radius $4$ units. [ ${ C }_{ 2 }$ is shown Blue.]

Murlidhar Sharma
Apr 2, 2015

C1 is a circle with center (0,1) and radius 2 units, in the Argand Plane. C2 is a circle with center (1,2) and radius 4. The rest is easy!