In this lecture, we will learn how to perform mathematical operations on complex numbers, these important
methods are addition and subtraction, multiplication and division.
And we have already learned these methods in theory, and we have performed by hand how to add and subtract
the complex numbers and how to find the multiplication and division of the complex domain.
So let's start with the addition.
So if we want to add these two numbers two plus three and simplify it, we just need to type Zetland
plus in Python and Python will do all the calculation.
So if we learn this, we will get nine plus eight.
So what does it mean, nine plus 30?
So basically during addition to is added to the seven, that is really part is the entry is added with
five that is added with the imaginary one in the same way we can perform the selection of these two
numbers in.
No multiplication and division.
Let's start with the multiplication.
So if we want to multiply two plus three with seven described it so similar to the addition, we have
to perform our replication by placing the static between these two complex number.
And I will do all the calculations for you.
So if we run this cell, we will get minus one plus thirty one day.
So this is the same answer that you got in your two selected.
So you have multiplied step by step these two complex numbers into three and you've got minus one plus
Heidi.
And so here in Python, it is very easy to multiply these complex number and see that we are getting
the same answer.
Now, how to find a complex conjugate in a python.
So if a number is a complex number is four plus T.G., then we have to use a method in number, which
is Condee.
So and we got plenty of Z when we calculate that complex conjugate for us.
So if the number was four plus three, then we can see there is complex conjugate is four minus three.
So when we then descend we get four minus three to.
Not division.
Look at the difference between the division between perform in duty and here in Python.
In theory, we had to perform a lot of steps.
The first step was we had to multiply and divide with the complex conjugate of the denominator.
Now, here with Python division is also very simple.
Just Type Z one, slash Z two.
And Python will do all the calculations for let's run this cell and see the.
So this is the result of the division of settlement, and so here the settlement is four plus three.
So this number is settlement and the settle is seven plus five.
So in order to compare the result with our Tuti, let's do the division with these two.
So I copied this number and paste these numbers here so that we can get the same result, which we got
an opportunity to lessen the sell.
And now we can see that our result was one three nine.
The real part was one three nine two and the immunity part was white, four point one four eight six.
So this is the real part.
And you can see the G here.
This is the immunity part of this division.
So important, a mathematical operations are very easy and simple.
And in theory, you need some time to perform a mathematical operations, especially division and multiplication.
So the concept here is before going to Python, you must know the mathematics by hand of this complex
number.
Only then you will understand and enjoy the power of.