6-11i

Rule:

A + Bi is represented by the line segment that goes from the origin to
the point (A,B).  It has length r.

So,
6 - 11i is represented by the line segment that goes from the origin to
the point (6,-11)

So we draw that line segment and label it r in length:



Next we'll indicate the angle q starting
at the right hand of the x-axis going around counter-clockwise
to the line we just drew.  I'll indicate q with
a red arc: 



Next we draw a line from that point perpendicular to the x-axis.
I'll draw it in green:



That makes a right triangle, so we label the horizontal leg
as the x value of the point. That is, x = 6.  We label the
vertical leg the y -value of the point. That is y = -11 



Next we calculate the value of r using the Pythagorean theorem:







So we label the r as r = 



Next we calculate q

by first calculating the tangent of the reference angle,

and then placing it in the 4th quadrant.



Use the inverse tangent function on the calculator to find
the inverse tangent of  to get the reference angle:

reference angle = 61.38954033°

To get q in the 4th quadrant subtract
the reference angle from 360° and get 

q = 298.6° rounded to the nearest
tenth of a degree.

So we label q = 298.6°



Now the trigonometric form is

r(cosq + i·sinq)

and upon substituting, the final answer is

(cos298.6° + i·sin298.6°)

Edwin