### Video Transcript

The blue vector represents the
complex number π³ one. The green vector represents the
complex number π³ two. What does the red vector
represent?

Now, try not to worry too much that
the axis labels are not what youβre used to. Weβll consider this to be much like
an π₯π¦-plane. Weβve got two vectors, given by π³
one and π³ two. Then, if we look at the red line,
we see it travels from the initial point of π³ one to the terminal point β thatβs
the end point β of π³ two.

And when looking at vectors, I like
to think about them a little bit like a metro or a tube map. Sometimes we want to travel from
one station to another but canβt get directly there. And instead, we travel to an
intermediate station, change trains, and travel on to the final destination. Our final destination is the
same. We just had to go about it in a
different way. In this case, the ultimate
destination is from the point zero, zero to the point seven, one. Rather than going straight there
though, we traveled from zero, zero to two, three along the vector π³ one. And then we traveled from two,
three to seven, one along the vector π³ two.

In vector form, we say that our
journey is π³ one plus π³ two. Now, we can check this by looking
at the components of each vector. π³ one is given by the vector two,
three. To travel from the initial to the
terminal point of our second vector, we travel five right and two down. So its components are five,
negative two.

We said that we thought the red
vector was the sum of these. Two, three plus five, negative
two. Well, we find the sum of these
vectors by adding their component parts. We add two and five to give us
seven. Then we add three and negative two
to get one. So π³ one plus π³ two is seven,
one. And if we compare that to the red
vector, we see that is also seven, one. The red vector represents π³ one
plus π³ two.