Explain your answer and i'll mark the brainliest! which complex number is the graph showing?

a. 2√2(cos 7π/4 + i sin 7π/4)

b. 2√2(cos 150° + i sin 150°)

c. 2(cos 7π/4 + i sin 7π/4)

d. 2(cos 90° + i sin 90°)

A 2√2(cos 7π/4 + i sin 7π/4)

Step-by-step explanation:

A. 2√2(cos 7π/4 + i sin 7π/4)

2 sqrt(2) ( sqrt(2)/2 - sqrt(2)/2 i)

Distribute

  2-2i

This is in the fourth quadrant  

B. 2√2(cos 150° + i sin 150°)

2 sqrt(2) (-sqrt(3)/2 +1/2i)

-sqrt(6) +sqrt(2) i

This is in the third quadrant (NO)

C. 2(cos 7π/4 + i sin 7π/4)

2( ( sqrt(2)/2 - sqrt(2)/2 i))

sqrt(2) - sqrt(2) i

This is the fourth quadrant

D. 2(cos 90° + i sin 90°)

2(0+i)

2i

This is on the positive y axis  NO

Now we need to decide between the two in the fourth quadrant.

The point has an x coordinate of 2 and a y coordinate of -2

This aligns with point A

(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

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: