- #1

danago

Gold Member

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**Given that [tex]|z-1+i| \le 1[/tex], find the maximum and minimum value of |z| and Arg(z).**

I realise that the equation given defines the interior of a circle of radius 1 centered at (1,-1), which includes the circumference.

For the first part of the question, i am able to represent the equation graphically. From what i understand, |z| is the distance from the origin to any point lying on or within the circle. If this is the case, i can see the minimum and maximum points, but im not too sure on how to calculate their locations.

For the next part, finding the extreme values of Arg(z), i just read straight from my graph and said that the minimum is [tex]-\pi/2[/tex] and the maximum is 0. Is that right?

Thanks in advance,

Dan.