00:02
All right, so we're asked to represent the complex number 5 minus 5i graphically and to write it in trigonometric form.
00:13
And so to graph this number, we're going to use the fact that in the form of a plus b .i for a complex number, its point can be represented as the point a -b on the complex plane.
00:38
And so for 5 minus 5i, that means that our a is just going to be 5, positive 5, and our b will be negative 5.
00:53
And so that means that on the complex plane, the number would be represented with the point 5 negative 5.
01:08
And so on the complex plane, we just go 5 to the right on the real axis and 5 down on the imaginary axis.
01:17
So our point will be about right here, 5 -5.
01:23
And recall that the trigonometric form of a complex number is in the form r times cosine data plus i.
01:45
Sign data where r is the absolute value and can be found with this definition, r equals a squared plus b squared, and data can be found through the fact that tan data is b over a.
02:21
So we can use these two rules in order to represent the complex number in trigonometric form.
02:28
So first of all, we're going to find r.
02:31
And so r, in our case, will be since a equals 5, 5 squared, plus and b equals negative 5, so negative 5 squared...