Q58P - Mathematical Methods in Physical Sciences

Question

Describe geometrically the set of points in the complex plane satisfying the following equations.

 $\mathbf{R}\mathit{e}\mathbf{\left(}\mathit{z}\mathbf{\right)}\mathbf{>}\mathbf{2}$. 

Step-by-Step Solution

Answer

This is the equation of the plane starting from the point $x=2$.

Step 1: Given Information

The equation is  $\mathrm{Re}\left(z\right)>2$.

Step 2: Definition of the Complex number

A complex number can be represented as:

 
$\mathit{z}\mathbf{=}\mathit{x}\mathbf{+}\mathit{i}\mathit{y}$
   

 

Where z is the complex number, x and y are real numbers, and i is known as iota, whose value is  $\sqrt{\mathbf{-}\mathbf{1}}$.

 

The modulus of a complex number can be calculated as:

 

$\mathbf{\left|}\mathbf{z}\mathbf{\right|}\mathbf{=}\sqrt{{\mathbf{x}}^{\mathbf{2}}\mathbf{+}{\mathbf{y}}^{\mathbf{2}}}$

Step 3: Find the value

The equation is $\mathrm{Re}\left(z\right)>2$.

 

The complex number is $z=x+yi$.

$\begin{array}{l}z=x+yi\\ \mathrm{Re}\left(z\right)=x\\ x>2\end{array}$ 

 

Hence, this is the equation of the plane starting from the point  $x=2$.