For 7, there are quite a few different ways to write each. For d, you could use the intersection of two circles, but that would take a bit of guessing, so let's use a couple of rays.
So, first we need to find the angle that the line makes with the x-axis. Given the ratio
=\frac{3}{2})
, we can see that this angle is approximately 56.3 degrees. So, this gives us:
=56.3^\circ\})
But there's two problems with this situation - it doesn't include the part of the line that goes down, nor the point (-2,0). So, we can find the part of the line that goes down by taking 180 - 56.3, and then we just need to include the point (-2,0). This can be written as:
=56.3^\circ\}\cup\{z:Arg(z+2)=126.4^\circ\}\cup\{(-2,0)\})
For e, we have a very simple ray, such that it starts at the point (1,0) and makes an angle of 45 degrees. This gives us:
=45^\circ\})
For the next two, you simply need to take the equations and - using a lot of algebra - simplify it like any other. Using the first equation as an example:
^2 + (y - 1)^2} + \sqrt{(x+1)^2+(y+1)^2} = 4)
I would then suggest moving one of the roots to the other side, it will make things easier to work with. Have fun!
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