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So I have explained to you already in the previous lecture that Python handles data types in a very

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convenient manner.

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For example, if we divide two integer numbers, it will give us a floating point number, which is

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very convenient because then we don't have to be careful what we're doing.

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So we can just write whatever we want to do, and it gives us the correct results.

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So let's discuss a bit more the different data types and especially who will start with the numbers.

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So we will discuss integer float and complex data types.

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So for example, when we write five, then of course it will be a five and integer number.

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But if we write 5.0, even though it's mathematically speaking exactly the same thing, the output will

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be 5.0.

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And you can see that both of these have different data types.

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So the five is an integer number and the 5.0 is a floating point number.

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So as I mentioned, there is really no need to define the data type.

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Python is really handy and using or in dealing with these data types in a very convenient manner, and

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it does everything automatically.

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So we can, for example, just add these two numbers five integer and floating point five, and the

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result will be a floating point ten.

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So if for whatever reason, you want to convert different data types from one to another.

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This is, of course, possible.

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For example, this could be useful for creating some output where the result would be just 10.

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And instead, the output would normally be expressed as ten point zero.

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So then in this case, you could, for example, turn this into an integer number so we can turn integer

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numbers into floating points numbers and we can do it the other way around.

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And here you must be a bit careful because if you try to transform a floating point number that is not

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dot zero into an integer number, then of course you will lose some information.

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You will make a small error.

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So this will not really round the number, but we'll just cut off the floating point number, so all

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of the digits after the comma or the dots.

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So in this case, int of 5.9 is just five.

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If you want to really do mathematical around operation, then you're right around five point nine and

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then it will give you six.

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So now we know about integer data type and float data type and something that's also very important,

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especially for physics programming is complex numbers.

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So the complex data type, so I hope you know this, that a complex number consists out of a real part

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and an imaginary part, and the imaginary part is just a floating point number, a real number multiplied

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by the imaginary unit.

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So in mathematics, this unit is called Are you?

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But in Python, it's called Jane.

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So if you're just right, Jane, there's a bit of a problem because J is not defined, it just means

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could mean a variable that we could define, for example, J for one.

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So if you want to have the imaginary unit I or in Python J and you must write something like one J.

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Or you must write something like two g.

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So special property.

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Sorry, I didn't take so long.

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So the special property of this imaginary unit is that the square of this number is negative.

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It's minus one.

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So if you run this, you will see the result is minus one plus zero g, so basically just minus one.

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So this allows us to calculate the square root of a negative number.

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So, for example, we could write and, um, pi square root of minus one.

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Um, and it tells us there is an invalid number, but what we could do is something like this

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because then we tell our computer or our Python program that we want to consider complex numbers.

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So in this case, there's minus one has the data type of a complex so we can calculate the square root,

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which will then be J.

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Or in mathematical language, the imaginary unit I sent.

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The type of such a complex number is, of course, complex, and we can, of course, to all the basic

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mathematical operations, for example, multiplication.

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So if we multiply these two complex numbers here.

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We get another complex number, and the result will be the real part is three times one, which is three.

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And then the other contribution to the real part would be five eye times too high, which would be 10.

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I squirt.

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So I squared, it's minus one.

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So this is minus 10.

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So we have three minus 10 as minus seven.

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And then for the imaginary part, we have two terms.

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So we have five times one, which is five.

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And we have three times too high, which is six I.

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So we have five plus six I, which is 11 I.

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So you see, we can really do all of the operations using complex numbers, but also you see that sometimes

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we must be careful because here we had the problem when we wrote and p square root of minus one gave

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us a mistake.

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But if we write this as a complex number, then it works.

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So let's see if this works.

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Oh, sorry, forgot the brackets.

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So now it works.

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So if we turn the real number or the integer number into a complex number, then you can use the square

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root command.

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So sometimes when using complex numbers, you must be a bit careful with the data types.

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But most of the times Python will manage all of these things just fine, and you don't need to watch

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out for some problems like you have to do in other programming languages.