PLOT THE COMPLEX NUMBER IN THE COMPLEX PLANE

Plot all four points in the same complex plane.

Example 1 :

1 + 2i, 3 - i, -2 + 2i, i

Solution :

Given, complex numbers are 1 + 2i, 3 - i, -2 + 2i, i

We are taking the real part of the complex number on the x-coordinate and the imaginary part on the y-coordinate.

Then, the ordered pair of the complex numbers are

So, the four points are (1, 2), (3, -1), (-2, 2) and (0, 1).

By plotting the four points on the complex plane, we get

Example 2 :

2 - 3i, 1 + i, 3, -2 - i

Solution :

Given, complex numbers are 2 - 3i, 1 + i, 3, -2 - i

Then, the ordered pair of the complex numbers are

So, the four points are (2, -3), (1, 1), (3, 0) and (-2, -1).

By plotting the four points on the complex plane, we get

Example 3 :

Find the distance between two complex numbers z₁  =  2 + 3i and z₂  =  7 - 9i on the complex plane.

Solution :

Given, z₁  =  2 + 3i and z₂  =  7 - 9i are complex numbers.

Then, the ordered pair of the complex numbers are

z₁  =  (2, 3) and z₂  =  (7, -9)

Now, we have the two points (2, 3) and (7, -9)

By plotting the two points on the complex plane, we get

Finding the distance  :

Formula for distance,

d  =  √[(x₂ - x₁)² + (y₂ - y₁)²]

(2, 3)----->(x₁, y₁)

(7, -9)----->(x₂, y₂)

d  =  √[(7 - 2)² + (-9 - 3)²]

d  =  √[(5)² + (-12)²]

d  =  √(25 + 144)

d  =  √169

d  =  13 units

So, the distance is 13 units.

Example 4 :

Find the distance and midpoint between two complex numbers z  =  3 + i and w  =  1 + 3i on the complex plane.

Solution :

Given, z  =  3 + i and w  =  1 + 3i are complex numbers.

Then, the ordered pair of the complex numbers are

z  =  (3, 1) and w  =  (1, 3)

Now, we have the two points (3, 1) and (1, 3)

By plotting the two points on the complex plane, we get

Finding the distance :

Formula for distance,

d  =  √[(x₂ - x₁)² + (y₂ - y₁)²]

(3, 1)----->(x₁, y₁)

(1, 3)----->(x₂, y₂)

d  =  √[(1 - 3)² + (3 - 1)²]

d  =  √[(-2)² + (2)²]

d  =  √(4 + 4)

d  =  √8

d  =  2√2 units

So, the distance is 2√2 units.

Finding the midpoint :

Formula for midpoint,

M  =  [(x₁ + x₂)/2, (y₁ + y₂)/2]

=  [(3 + 1)/2, (1 + 3)/2]

Midpoint  =  (2, 2)

So, the midpoint is (2, 2)

Example 5 :

Find the distance and midpoint between the complex number z  =  5 + 2i and its conjugate z^-  =  5 - 2i on the complex plane.

Solution :

Given, z  =  5 + 2i and z^-  =  5 - 2i are complex numbers.

Then, the ordered pair of the complex numbers are

z  =  (5, 2) and z^-  =  (5, -2)

Now, we have the two points (5, 2) and (5, -2)

By plotting the two points on the complex plane, we get

Finding the distance :

Formula for distance,

d  =  √[(x₂ - x₁)² + (y₂ - y₁)²]

(5, 2)----->(x₁, y₁)

(5, -2)----->(x₂, y₂)

d  =  √[(5 - 5)² + (-2 - 2)²]

d  =  √[(-4)²]

d  =  √16

d  =  4 units

So, the distance is 4 units.

Finding the midpoint :

Formula for midpoint,

M  =  [(x₁ + x₂)/2, (y₁ + y₂)/2]

=  [(5 + 5)/2, (2 - 2)/2]

Midpoint  =  (5, 0)

So, the midpoint is (5, 0)

Related pages

• Dividing complex numbers
• Multiplication of complex numbers

Apart from the stuff given above,  if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.