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The minimum |z| satisfying |z+1/z| = 2 is ...........? The minimum |z| satisfying |z+1/z| = 2 is ...........?
Put z = x+iy=> |x + iy + 1/(x + iy)|=> |[(x+iy)^2 + 1]/(x+iy)|=>|x^2 – y^2 + 2xyi + 1|/|x+iy|=> root[(x^2 – y^2 +1)^2 + 1]/root(x^2 + y^2)Now solve it and compare it.
Please read the question again. I want to find the minimum |z| Please tell me how to use Triangle Inequality in this..
The answer is -1+ as shown below......................................................................................
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