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Complex Number Graphing Question

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epherbertson:
Hi. I am completely lost for question 14b. I tried looking through my teachers solution and it still didn't make much sense. Any help is appreciated

wyzard:

--- Quote from: epherbertson on January 25, 2017, 10:46:58 pm ---Hi. I am completely lost for question 14b. I tried looking through my teachers solution and it still didn't make much sense. Any help is appreciated


(Image removed from quote.)

--- End quote ---

Damn this is a sick question, took me quite a while to figure it out :P The graph for 14b is a circle with a radius of 2.

I'll give you a crucial hint, make us of the following theorem:
An angle inscribed in a semicircle is always a right angle


This should give you some idea on how to work it out 8)

RuiAce:


GeoGebra
Eddie Woo teaching it in a very understandable manner. Or I think so at least - I never understood this locus and only briefly understood it watching his video. Note that he uses a specific example.

tissue:
sorry in advance for the formatting,

This was how I was taught.

arg(z-z0) - arg(z-z1) = θ

is a locus that can either be a major arc, minor arc, straight line or a semi-circle. This all depends on the angle θ.
an angle between 0 and π/2 would be a major arc, an angle of π/2 would be a semi-circle, an angle between π/2 and π would be a minor arc while an angle of π would be a straight line from one point to another, excluding those points. This would all be drawn in an anti-clockwise direction starting from z0 and ending at z1.

So basically, you end up with a semi-circle with its middle cut off from point (2,0) to point (-2,0) and an internal angle of π.

I remembered these by heart so when I got into the exam I was confident enough to draw these instead of solving algebraically. I have a sheet of notes on all of the possible questions that I can find if you need me to.

RuiAce:

--- Quote from: tissue on January 26, 2017, 03:13:46 am ---is a locus that can either be a major arc, minor arc, straight line or a semi-circle. This all depends on the angle θ.
an angle between 0 and π/2 would be a major arc, an angle of π/2 would be a semi-circle, an angle between π/2 and π would be a minor arc while an angle of π would be a straight line from one point to another, excluding those points. This would all be drawn in an anti-clockwise direction starting from z0 and ending at z1.

--- End quote ---
Watch Eddie Woo's videos. This all gets expained.

--- Quote from: tissue on January 26, 2017, 03:13:46 am ---I remembered these by heart so when I got into the exam I was confident enough to draw these instead of solving algebraically. I have a sheet of notes on all of the possible questions that I can find if you need me to.

--- End quote ---
You definitely should not be doing this one algebraically.

Don't be resistant to watch the video. That guy is a really famous teacher.

I'm not linking a video just to be lazy. It's because I genuinely cannot explain it as well as he does.

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