### Video Transcript

The figure shows a locus of a point
π§ in the complex plane. Write an equation for the locus in
the form the argument of π§ minus π over π§ minus π equals π, where π and π,
which are complex numbers, and π, which is greater than zero and less than or equal
to π, are constants to be found.

Remember, the locus of a point π§
in this form is the arc of a circle which subtends an angle of π between the points
represented by π§ one and π§ two. We have three conditions on π. If itβs less than π by two, the
locus is a major arc. If itβs equal to π by two, itβs a
semicircle. And if itβs greater than π by two,
the locus is a minor arc. And, remember, the endpoints are
not part of this locus. We can see by looking at the
diagram that the locus of our π§ is the major arc of a circle. And this makes sense because π is
equal to π by five radians.

The endpoints of our locus lie at
π΄ and π΅ whose Cartesian coordinates are four, negative three and negative three,
one, respectively. These represent the complex numbers
four minus three π and negative three plus π. And, remember, this locus is traced
in a counterclockwise direction. Since the starting point is that
represented in the complex number four minus three π, we can say that the equation
of our locus is the argument of π§ minus four minus three π over π§ minus negative
three plus π equals π by five. We were actually told to find the
value of the constants π, π, and π. π is four minus three π, π is
negative three plus π, and π is π by five.