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i struggle with the first function, please help thanks

 May 11, 2019

Best Answer 

 #1
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\(|z-3i|\leq 1\\ \text{describes a disk centered at }(0,3i) \text{ of radius }1\\ 0\leq \arg(z-3i)\leq \dfrac \pi 2\\ \text{says to only consider the first quadrant of that circle}\\ \text{The full circle will have area }\pi (1)^2 = \pi\\ \text{The first quadrant of this circle will have area }\dfrac \pi 4\)

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 May 11, 2019
 #1
avatar+5662 
+2
Best Answer

\(|z-3i|\leq 1\\ \text{describes a disk centered at }(0,3i) \text{ of radius }1\\ 0\leq \arg(z-3i)\leq \dfrac \pi 2\\ \text{says to only consider the first quadrant of that circle}\\ \text{The full circle will have area }\pi (1)^2 = \pi\\ \text{The first quadrant of this circle will have area }\dfrac \pi 4\)

Rom May 11, 2019
 #2
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oh right is it because arg(z-3i) describes where the half line region starts

Guest May 11, 2019

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