Wikipedia:Reference desk/Archives/Mathematics/2016 September 16

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September 16

2i to the power of 4n

Go to http://puzzle.queryhome.com/13263/what-number-when-multiplied-itself-same-answer-added-itself

What does 2i to the 4n mean?? Is the n a special value or just a variable?? In the latter case, then 2i to the 4n (assuming n is an integer) is 16 to the n, and thus it can be re-written as 16^n. Any corrections?? Georgia guy (talk) 00:52, 16 September 2016 (UTC)

You are presumably referring to the March 4 answer by Nithi Mani, who comes up with the two solutions 2 and 0 by inspection (and these are the only two solutions of the quadratic x² = 2x over either the reals of the complex numbers), but then also claims, by inspection, that since nothing was mentioned about an imaginary part, then 2(i)^(4n) is also a solution. Note the parentheses here. They are saying 2i⁴ⁿ, not (2i)⁴ⁿ as you interpreted. But 2i⁴ⁿ = 2 for any integer n. So this is one of the original two solutions of this quadratic equation. If they aren't making a joke, it would appear that Nithi Mani hadn't understood equality of complex numbers back in March. -- ToE 02:33, 16 September 2016 (UTC)

What a cliffhanger. We're dying to know if he has improved his understanding of complex number equality by now! -- Meni Rosenfeld (talk) 10:35, 16 September 2016 (UTC)