Addition and subtraction of complex numbers. Hello friends, today it’s all about the addition and subtraction of complex numbers.

Have a look!!

### Addition and subtraction of complex numbers

Suppose I have two complex numbers and . Also, the number is and the number is . Now here shows the imaginary part of the number.

So I can say if any number is , then in the complex number form it is . Similarly, if there is a number, say, , then in the complex number form it will be .

Anyway, now I go back to the complex numbers and .

Now when I want to add the two complex numbers, the rule is that the real parts will go together. And the imaginary parts will be together.

So that means, in this case, I’ll add the real part of to the real part of . Also, I’ll add the imaginary part of to the imaginary part of .

Thus it gives

Now the same thing also happens with the subtraction of complex numbers.

So becomes

Now I’ll give some examples on that.

If interested, you can read more about the other posts in complex numbers such as the multiplication and division of complex numbers.

#### Solved examples of addition and subtraction of complex numbers

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 Kreyszig (2005)* “Let and . Showing the details of your work, find (in the form of ): . ”

##### Solution

Now here I have the two complex numbers as and . And I have to find out the value of .

First of all, I’ll get the value of . So it will be

Now I’ll simplify it to get

As I have mentioned above, the real part of goes with the real part of . Similarly, the imaginary part of goes with the imaginary part of .

So it will look like

Thus it becomes

Hence the value of will be

Therefore I can conclude that this is the answer to this example.

Now I’ll give another example.

##### Example 2

According to Kreyszig (2005)* “Let and . Showing the details of your work, find (in the form of ): . ”

##### Solution

Now in this case, the two complex numbers are and . And I have to find out the value of .

First of all, I’ll get the value of . So it will be

Now I’ll simplify it to get

As I have mentioned earlier, the real part of goes with the real part of . Similarly, the imaginary part of goes with the imaginary part of .

So it will look like

Thus it becomes

Hence the value of will be

Now I’ll expand the right-hand-side of this expression to get

Next, I’ll simplify it to get

As I already know that , hence the expression will be

So this gives

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

Dear friends, this is the end of my 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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