# |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...

Jan 14, 2018

Circle

#### Explanation:

Consider
Z = x + iy
therefore |z| = ${\left({x}^{2} + {y}^{2}\right)}^{\frac{1}{2}}$
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 $\left(0 , 0\right) \text{ radius } = 2$

#### Explanation:

$| z | = 2$

$z = x + i y$

so replace $z \text{ with } x + i y$

$\therefore | z | = | x + i y |$

by definition

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

$| z | = 2 \implies \sqrt{{x}^{2} + {y}^{2}} = 2$

${x}^{2} + {y}^{2} = 4$

circle centre $\left(0 , 0\right) \text{ radius } = 2$

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 $\left(x + i y\right)$, where $x \mathmr{and} y$ are real numbers. Inserting in LHS of given equation we get

$| z {|}^{2} = z {z}^{\text{*}}$$= \left(x + i y\right) \left(x - i y\right) = {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 $= 2.$