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.
Answer:
y=-2x +1
Step-by-step explanation:
hope this helps
-10 and -1 multiply to get 10 and add to get -11
You have to times it by 100 - however much you want to decrease it by so your multiplier would 0.38
Answer:
Y-intercept = 13
Step-by-step explanation:
Since, given points are:
(-2,5) and (3,25)
Now, by slope intercept form:
y= mx + b
Here, m= slope and b= y-intercept
In order to find y-intercept, we must find slope firstly:
Since,
Slope= m= y2-y1 / x2-x1
m= 25 - 5 / 3 - (-2)
m= 20 / 5
m= 4
Put ‘m’ in slope intercept form:
y= 4x + b
Substitute either point into above equation:
25= 4(3) +b
25= 12 + b
25 - 12 = b
or b= 25 - 12
b= 13
Hence, y-intercept is 13.
