www.mathcentre.ac.uk/.../05-MultiplyingF61Mb.mp4

In this unit, went to look at
how to multiply 2 complex

numbers together. And
multiplying two complex numbers

simply requires us to be able to
multiply out brackets to collect

together like turns, and to
remember that I is the special

number whose property is that I
squared is equal to minus one.

So let's look at how that
all works in an example.

So here we have two complex
numbers 4 + 7 I.

And 2 + 3 I and we're going to
do is going to multiply these

two complex numbers together.

And the first thing we do is we
just multiply out the brackets

so we each term in the first
bracket must multiply each term

in the SEC bracket.

So we have 4 * 2 which is 8.

Four times plus three I, which
is plus 12 I.

Plus Seven I times two is

plus 49. And plus Seven
I times plus three. I is

21. I squared.

Now we see straight away that we
would be able to combine these

two terms because they're both
terms with eyes in them.

So the the front is going to
stay the same plus 12 I plus

14. I gives us plus 26 I.

Now over this term, on the end,
which is 21, I squared. Now we

have to remember what we know
about I. I is the square root of

minus one or said another way I
squared is equal to minus one.

So in this term 21 I squared we
can replace the isquared by

minus one. So that's plus 21
times minus one.

Now 21 times minus one is minus
21, so we have 8 - 21. You can

combine those two terms.

8 - 21 is

minus 13. Plus the
26 I was already there.

And so our answer, when we
multiply these two complex

numbers together, is this new
complex number minus 13 + 26? I

OK? We're going to look at
another example, two different

complex numbers. This time the
complex numbers minus 2 + 5. I

first one on 1 - 3 I is the
second one, exactly the same

principles before, but we have
to be a bit more careful 'cause

we got lots of minus signs

floating about. So we multiply
out the brackets minus 2 * 1.

Is minus 2.

Minus two times minus three I
gives us plus 6I.

Plus 5I Times one gives us

plus 5I. And plus 5I
Times minus three I years, minus

15 I squared.

Now we combine together our
items so we have minus 2 + 6

I plus 5I, giving us plus 11 I.

And in this term, remember that
I squared is minus one, so this

is minus 15 times minus one,
which is plus 15.

And so the final thing we do is
combine the minus two and the

plus 15 to get plus 13 and then
plus 11 I.

And so our answer, we multiply
these two complex numbers

together is the complex number
13 + 11 I.

So that's how we multiply
together to complex numbers

in the next unit. We're going
to look at a property that

complex numbers have called
the complex conjugate.