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.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

i dont have an answer

step-by-step explanation: