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

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In this unit, went to look at
how to multiply 2 complex
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numbers together. And
multiplying two complex numbers
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simply requires us to be able to
multiply out brackets to collect
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together like turns, and to
remember that I is the special
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number whose property is that I
squared is equal to minus one.
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So let's look at how that
all works in an example.
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So here we have two complex
numbers 4 + 7 I.
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And 2 + 3 I and we're going to
do is going to multiply these
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two complex numbers together.
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And the first thing we do is we
just multiply out the brackets
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so we each term in the first
bracket must multiply each term
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in the SEC bracket.
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So we have 4 * 2 which is 8.
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Four times plus three I, which
is plus 12 I.
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Plus Seven I times two is
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plus 49. And plus Seven
I times plus three. I is
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21. I squared.
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Now we see straight away that we
would be able to combine these
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two terms because they're both
terms with eyes in them.
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So the the front is going to
stay the same plus 12 I plus
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14. I gives us plus 26 I.
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Now over this term, on the end,
which is 21, I squared. Now we
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have to remember what we know
about I. I is the square root of
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minus one or said another way I
squared is equal to minus one.
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So in this term 21 I squared we
can replace the isquared by
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minus one. So that's plus 21
times minus one.
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Now 21 times minus one is minus
21, so we have 8 - 21. You can
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combine those two terms.
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8 - 21 is
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minus 13. Plus the
26 I was already there.
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And so our answer, when we
multiply these two complex
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numbers together, is this new
complex number minus 13 + 26? I
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OK? We're going to look at
another example, two different
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complex numbers. This time the
complex numbers minus 2 + 5. I
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first one on 1 - 3 I is the
second one, exactly the same
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principles before, but we have
to be a bit more careful 'cause
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we got lots of minus signs
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floating about. So we multiply
out the brackets minus 2 * 1.
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Is minus 2.
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Minus two times minus three I
gives us plus 6I.
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Plus 5I Times one gives us
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plus 5I. And plus 5I
Times minus three I years, minus
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15 I squared.
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Now we combine together our
items so we have minus 2 + 6
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I plus 5I, giving us plus 11 I.
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And in this term, remember that
I squared is minus one, so this
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is minus 15 times minus one,
which is plus 15.
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And so the final thing we do is
combine the minus two and the
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plus 15 to get plus 13 and then
plus 11 I.
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And so our answer, we multiply
these two complex numbers
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together is the complex number
13 + 11 I.
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So that's how we multiply
together to complex numbers
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in the next unit. We're going
to look at a property that
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complex numbers have called
the complex conjugate.
Title:
www.mathcentre.ac.uk/.../05-MultiplyingF61Mb.mp4
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