Abhimanyu B.

# Need help with complex numbers and locus

part1. Let z=rcisθ where 0<θ<pi. show that Arg(z^2)=2θ.

part2. sketch the region defined by {z: Arg(z^2)>pi/2}
in the answers it shows region pi/4 to pi/2 and region 5pi/8 to 3pi/2 should be shaded which I dont understand why these regions must be shaded.
Thanks for the help in advance

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Abhimanyu B.

Hi thanks for the answer, that was very helpful. can you help with part 2?
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01/22/18

Kenneth S.

I can see that if theta is in (0,pi) and arg (z2) = 2θ then 2θ > pi/2 means θ > pi/4.