Representing Complex Numbers on the Complex Plane page 9

Procedure for Plotting Complex Numbers on the Complex Plane

• Overview of the Complex Plane:

  • A complex number is expressed in standard form as $a + bi$, where $a$ represents the real part and $b$ represents the coefficient of the imaginary part.

  • The complex plane utilizes a two-dimensional coordinate system where the horizontal axis represents the real part and the vertical axis represents the imaginary part.

• Step-by-Step Procedure:

  • Step 1: Determine the real part and the imaginary part:

  • Identify the real component $a$ and the imaginary component $b$ from the given complex number $a + bi$.

  • Step 2: Move along the horizontal axis:

  • Move along the horizontal axis to show the real part $a$ of the complex number.

  • Step 3: Move parallel to the vertical axis:

  • Move parallel to the vertical axis to show the imaginary part $b$ of the complex number.

  • Step 4: Plot the point:

  • Mark and plot the point corresponding to $(a, b)$ on the complex plane.

Worked Example: Plotting a Complex Number

• Problem Statement:

  • Plot the complex number $3 - 4i$ on the complex plane.

• Detailed Solution Breakdown:

  • Step 1: Determine the real part and imaginary part:

  • Real part = $3$

  • Imaginary part = $-4$

  • Step 2: Horizontal displacement:

  • Move $3$ units to the right along the horizontal axis.

  • Step 3: Vertical displacement:

  • Move $4$ units down parallel to the vertical axis because the imaginary component is $-4$

  • Step 4: Plotting:

  • Plot the point corresponding to $(3, -4)$ on the complex plane.