|COMPLEXE NUMBERS| What is the geometrical representation of |z| = 2? Thank you!

Hello! I don't get this because I thought you needed an angle to solve this? Obviously, that is probably not the case...

3 Answers
Jan 14, 2018

Circle

Explanation:

Consider
Z = x + iy
therefore |z| = (x^2+y^2)^(1/2)
also |z| = 2
hence x^2+y^2=4
therefore it represents a circle
Hope u find it helpful :)

Jan 14, 2018

x^2+y^2=4

circle centre (0,0) " radius "=2

Explanation:

|z|=2

z=x+iy

so replace z" with "x+iy

:.|z|=|x+iy|

by definition

|x+iy|=sqrt(x^2+y^2

|z|=2=>sqrt(x^2+y^2)=2

x^2+y^2=4

circle centre (0,0) " radius "=2

Jan 21, 2018

For any complex number z, to calculate its modulus |z|, the number needs to multiplied with its complex conjugate to obtain |z|^2.

Let z be of the type (x+iy), where xand y are real numbers. Inserting in LHS of given equation we get

|z|^2=zz^"*"=(x+iy)(x-iy)=x^2+y^2

Now the given equation becomes

sqrt(x^2+y^2)=2

Squaring both sides we get

x^2+y^2=4

The equation represents a circle with center at the origin and radius =2.