Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 October 23rd, 2016, 08:29 PM #1 Member   Joined: Sep 2016 From: zambia Posts: 31 Thanks: 0 sets of numbers (complex numbers) Show that (1+i/1-i)^4k=1 if k is a positive integer October 23rd, 2016, 08:52 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,646 Thanks: 1476 is this supposed to be $\left(\dfrac{1+i}{1-i}\right)^{4k}$ or $\left(1+\dfrac{i}{1-i}\right)^{4k}$ or possibly $\left(1 + \dfrac {i}{1} -i\right)^{4k}$ October 23rd, 2016, 09:55 PM   #3
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Quote:
 Originally Posted by romsek is this supposed to be $\left(\dfrac{1+i}{1-i}\right)^{4k}$
I guess it's supposed to be this

$\dfrac{1+i}{1-i} = \dfrac{1+i}{1-i}\dfrac{1+i}{1+i}=\dfrac{2i}{2}=i$

$i^4 = 1$

$i^{4k} = (i^4)^k = 1^k = 1$

$\left(\dfrac{1+i}{1-i}\right)^{4k} = 1$ Tags complex, numbers, sets Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post dazedAndConfused Math 3 July 1st, 2015 09:07 AM ziggy Algebra 11 February 15th, 2015 12:42 AM jonas Complex Analysis 2 October 13th, 2014 04:03 PM rajemessage Probability and Statistics 11 August 21st, 2014 03:05 PM Mathforum1000 Number Theory 2 June 20th, 2012 05:18 PM

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