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July 11th, 2016, 04:58 AM  #1 
Newbie Joined: Jul 2016 From: Belgium Posts: 3 Thanks: 0  complex numbers
Hello, I had a little trouble in finding the solution and the howtosolveit of ((1i).(1i)^(1) )=1 Can someone help me, please? Kind regards, V. 
July 11th, 2016, 05:18 AM  #2 
Senior Member Joined: Dec 2015 From: holland Posts: 163 Thanks: 37 Math Focus: tetration 
it is false 1/((1  i )^2) is not 1

July 11th, 2016, 05:29 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond 
It is true. $\displaystyle (1i)(1i)^{1}=\dfrac{1i}{1i}=1$ Where's the difficulty? 
July 11th, 2016, 06:11 AM  #4 
Newbie Joined: Jul 2016 From: Belgium Posts: 3 Thanks: 0 
I got that far too but I couldn't believe it would be that easy.. Just thought there was a catch somewhere.. 
July 11th, 2016, 09:38 AM  #5 
Senior Member Joined: Dec 2015 From: holland Posts: 163 Thanks: 37 Math Focus: tetration  oh i see (( 1  i )((1  i )^{1}))
Last edited by manus; July 11th, 2016 at 09:42 AM. 
July 11th, 2016, 11:07 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
If you want to do it the "hard way" $\displaystyle (1 i)^{1}= \frac{1}{1 i}\frac{1+ i}{1+ i}= \frac{1+ i}{(1 i)(1+ i)}= \frac{1+ i}{2}$. Then $\displaystyle (1 i)(1 i)^{1}= \frac{(1 i)(1+ i)}{2}= \frac{2}{2}$. 

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