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proof-that-z-2-z-z-C-example-i-1-i-2-1-i-4-1-i-4-i-2-1-1-1-1-




Question Number 52200 by gunawan last updated on 04/Jan/19
proof that   (√z^2 ) ≠ z , z ∈ C  example  i=(√(−1))  i^2 =−1  i^4 =1  (√(i^4  )) ≠ i^2   (√1) ≠ −1  1 ≠ −1
$$\mathrm{proof}\:\mathrm{that}\: \\ $$$$\sqrt{{z}^{\mathrm{2}} }\:\neq\:{z}\:,\:{z}\:\in\:\mathbb{C} \\ $$$$\mathrm{example} \\ $$$${i}=\sqrt{−\mathrm{1}} \\ $$$${i}^{\mathrm{2}} =−\mathrm{1} \\ $$$${i}^{\mathrm{4}} =\mathrm{1} \\ $$$$\sqrt{{i}^{\mathrm{4}} \:}\:\neq\:{i}^{\mathrm{2}} \\ $$$$\sqrt{\mathrm{1}}\:\neq\:−\mathrm{1} \\ $$$$\mathrm{1}\:\neq\:−\mathrm{1} \\ $$$$ \\ $$

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