Find the orders of the following elements of the group C× = (C \ {0}, ×) of non-zero complexnumbers:(i) 1, (ii) −1, (iii) 3, (iv) i
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Solution 1
(i) The order of 1 in the group C× is 1. This is because 1 raised to any power is always 1, so the smallest positive integer n such that 1^n = 1 is 1.
(ii) The order of -1 in the group C× is 2. This is because (-1)^2 = 1, and 2 is the smallest positive integer such that (-1)^n = 1.
(iii) The order Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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