Multiplication and division of complex numbers. Hello friends, today it’s all about the multiplication and division of complex numbers. Have a look!!

### Multiplication and division of complex numbers

If you are looking for more in complex numbers, do check in:

**Addition and subtraction of complex numbers**

**Polar form of a complex number**

**Modulus and argument of a complex number**

**Functions of complex variables**

Suppose I have two complex numbers and

In one of my earlier posts, I have already talked about the addition and subtraction of complex numbers.

##### Multiplication of two complex numbers

Now I’ll multiply the two complex numbers

And this gives

Since

Now I’ll separate the real and imaginary parts to get

Next, I’ll show the division of complex numbers, that is

##### Division of two complex numbers

So

First of all, I’ll get rid of the imaginary part of the denominator. Therefore I can write it as

(1)

Now I’ll simplify

Thus it will be

(2)

Next, I’ll simplify

Thus it will be

Since

Now I’ll separate the real and imaginary parts to get

(3)

Thus I’ll substitute equations (2) and (3) to equation (1) to get the value of

Now I’ll give some examples on the multiplication and division of complex numbers.

#### Solved examples of multiplication and division 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

##### Solution

Now here I have to find out the values of

###### First part

First of all, I’ll find out the value of

So the value of

Now I’ll expand the right-hand side.

Thus it will be

Next, I’ll simplify it.

So it becomes

Since

Thus it will be

Hence I can say that

Now I’ll do the second part.

###### Second part

So here I have to find out the value of

As I already know that the real part of the complex number

Hence the value of

Therefore I can conclude that

Now I’ll give another example.

##### Example 2

According to Kreyszig (2005)* “Let

##### Solution

Now here the two complex numbers are

Thus it will be

As I have mentioned above, first of all, I’ll get rid of the imaginary part of the denominator. Therefore I can write it as

Next, I’ll simplify it. So it will be

Since

Hence I can simplify it a bit to get

Therefore I can conclude that

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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