You would start by finding the area of the circle and then finding the area of the rectangle. After finding both, subtract the area of the rectangle from that of the circle. <span />
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.
Factories both equations:
5(x - 4) / (x + 2)(x - 4)
Then take out the common brackets:
5 / x + 2
Minus 2 from both sides:
3 / x
If you are looking for the greatest common factor of the numerator and denominator, the answer would be (x - 4)
Answer:
Try D) rotation 180 degrees about the origin.
Step-by-step explanation:
When you look at it, it appears to move 180 degrees about that origin.
Hope this helps! Let me know!
