Express the complex number in trigonometric form. 2-2i

Step-by-step explanation:

Think of '2' as being on the positive x-axis and that -2i being on the negative y-axis.  The resultant of these two vectors has magnitude √(2²+[-2]²), which comes out to 2√2.  

Since the resultant of these two vectors lies in Quadrant IV, we measure the angle from the positive x-axis counterclockwise into Quadrant IV.  The positive angle associated with this is 315°; the negative one is -45°

We are now in a position to express 2 - 2i in trig form:

2√2 angle 315°

that is, the magnitude of this resultant vector is 2√2 and the vector, located in QIV, has the angle 315° as measured from the positive x-axis.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.