Map the points in the complex plane. Hello friends, today I’ll show you how to map the points in the complex plane. Have a look!!

**Map the points in the complex plane**

So have a look at these examples!!

**Solved examples of how to map the points in the complex plane**

Disclaimer: None of these examples are mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here is the first example.

**Example 1**

According to Stroud and Booth (2011)*, “Map the following point in the -plane onto the -plane under the transformation .

”

**Solution**

Now here the point is, say, . And I have to map this point in the -plane onto the -plane under the transformation . Also, the -plane is .

Now let’s say that

where is the real and is the complex part of .

Also, Therefore, for , will be

Next, I’ll simplify it to get

Then I’ll separate the real and the complex part to get

If I compare it with , I can say that

(1)

(2)

Now I’ll transform on the -plane.

If I compare with , I can say that

Next, I’ll substitute in equations (1) and (2) to get the image of the point on the -plane as

and

So the point transforms onto .

Thus the mapping of the point in the -plane onto the -plane under the transformation is .

Hence I can conclude that this is the answer to the given example.

Now I’ll give you another example.

**Example 2**

According to Stroud and Booth (2011)*, “Map the following point in the -plane onto the -plane under the transformation .

”

**Solution**

Now here the point is, say, . And I have to map this point in the -plane onto the -plane under the transformation . Also, the -plane is .

Now let’s say that

where is the real and is the complex part of .

Also, Therefore, for , will be

Next, I’ll simplify it to get

Since , I can say that

Then I’ll separate the real and the complex part to get

If I compare it with , I can say that

(3)

(4)

Now I’ll transform on the -plane. If I compare with , I can say that

Next, I’ll substitute in equations (3) and (4) to get the image of the point on the -plane as

and

So the point transforms onto .

Thus the mapping of the point in the -plane onto the -plane under the transformation is .

Hence I can conclude that this is the answer to the given example.

Now I’ll give you another example.

**Example 3**

According to Stroud and Booth (2011)*, “Map the following point in the -plane onto the -plane under the transformation .

”

**Solution**

Now here the point is, say, . And I have to map this point in the -plane onto the -plane under the transformation . Also, the -plane is .

Now let’s say that

where is the real and is the complex part of .

Also, . Therefore, for , will be

Next, I’ll simplify it to get

Since , I can say that

Then I’ll separate the real and the complex part to get

If I compare it with , I can say that

(5)

(6)

Now I’ll transform on the -plane. So I can say that

If I compare with , I can say that

Next, I’ll substitute in equations (5) and (6) to get the image of the point on the -plane as

and

So the point transforms onto .

Thus the mapping of the point in the -plane onto the -plane under the transformation is .

Hence I can conclude that this is the answer to the given example.

Now I’ll give you another example.

**Example 4**

”

**Solution**

Here the point is, say, . Now let’s say that

where is the real and is the complex part of .

Also, . Therefore, for , will be

Next, I’ll simplify it to get

Related post: **Multiplication of complex numbers**

Since , I can say that

Then I’ll separate the real and the complex part to get

If I compare it with , I can say that

(7)

(8)

Now I’ll transform on the -plane. If I compare with , I can say that

Next, I’ll substitute in equations (7) and (8) to get the image of the point on the -plane as

and

So the point transforms onto .

Hence I can conclude that this is the answer to the given example.

Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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