Answer: 1. Y
2.Y
3.N
Step-by-step explanation:
Answer:
Step-by-step explanation:
Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.
When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.
Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?
What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!
Putting all of this together gives us:
z = |mag|*(cos(angle) + isin(angle))
= 2*cos(270°) + isin(270°)).
To verify, let's consider what cos(270°) and sin(270°) are.
If you graph cos(x) and look at 270°, you get 0.
If you graph sin(x) and look at 270°, you get -1.
So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.
For lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically:
m1*m2=-1, and in this case:
-m/4=-1
-m=-4
m=4, so the slope of the perpendicular line is 4 so we have thus far:
y=4x+b, using point (-4,3) we can solve for the y-intercept, "b"
3=4(-4)+b
3=-16+b
19=b, so our line is:
y=4x+19
C
Step-by-step explanation:
Graphs are simple I would know trust me man
