Q52P - Mathematical Methods in Physical Sciences

Question

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

 $\mathit{R}\mathit{e}\mathbf{ }\mathit{z}\mathbf{=}\mathbf{0}$.

Step-by-Step Solution

Answer

The equation is the imaginary axis (y-axis).

Step 1: Given Information

The equation is $Re z=0$ .

Step 2: Definition of the Complex number

A complex number can be written as:

 

 $\mathrm{z}=\mathrm{x}+\mathrm{iy}$ 

 

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

 

The modulus of a complex number can be calculated as:

 $\left|Z\right|=\sqrt{x^2+y^2}$

Step 3: Find the value

The equation is $\mathrm{Re} \mathrm{z}=0$  .

 

 $$\begin{gathered} \mathrm{Re} \mathrm{z}=0 \\ x=0 \end{gathered}$$

 

Hence, the equation is the imaginary axis (y-axis).