Semi Circles on Argand Diagrams (2 of 3: Graphing the locus)

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In these questions, what is the maximum value of arg(z)? How to do it? Plz explain on next video.

Adheeba_firdhous
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Love the videos. Small question (will probably be answered in the next episode):
So this works because of Thale's theorem.
If we were to calculate some other angle (not 90°), does the exercise become too complicated or is there a similar trick?

tadejsivic