### Video Transcript

Simplify two ๐ all squared times negative two ๐ all cubed.

And in this particular question, ๐ isnโt just any old variable; it represents the
imaginary part of a complex number. So in other words, weโve got two imaginary numbers multiplied together.

Now remember, with imaginary numbers weโve defined, ๐ squared to be equal to
negative one. In other words, ๐ is the square root of negative one.

Okay, so letโs expand out our calculation. And two ๐ all squared times negative two ๐ all cubed means two ๐ times two ๐
times negative two ๐ times negative two ๐ times negative two ๐, so letโs multiply
these pairs of parentheses out. Two by two, well two ๐ times two ๐ equals four ๐ squared.

Oh remember, we said ๐ squared is equal to negative one, so we can replace that in
this part of the calculation here. This means four times negative one or negative four. Okay, letโs take the next two parentheses along. Weโre gonna do negative two ๐ times negative two ๐. Well negative two times negative two is positive four, and ๐ times ๐ is ๐
squared.

So that leaves us with negative four times four ๐ squared times negative two ๐. And again, we said ๐ squared is equal to negative one, so we can replace the ๐
squared with negative one. So that middle term is four times negative one, which is negative four.

Well now letโs multiply these two terms together: negative four times negative four
is positive 16. So weโve got 16 times negative two ๐, which just means 16 times negative two times
๐, and 16 times negative two is negative 32.

So weโve got negative 32๐. Now we canโt actually simplify that down any further, so
thatโs our answer: negative 32๐.