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given that \(\left | z - 2 \right |=2 \) and \(arg(z-2) = -\pi/3 \)

Express z in the form a+bi where a and b are real numbers 

 Feb 20, 2019
 #1
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\(\text{consider }\tilde{z} = z-2\\ |\tilde{z}|=2 \text{ and }\arg(\tilde{z}) = -\dfrac{\pi}{3}\\ \tilde{z} = 2 \cos\left(-\dfrac{\pi}{3}\right) + i 2 \sin\left(-\dfrac{\pi}{3}\right)\\ \tilde{z} = 1-i \sqrt{3},~\text{ and thus}\\ z = \tilde{z}+2 = 3 - i \sqrt{3}\)

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 Feb 20, 2019

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