We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
681
2
avatar

i^61 ???

 Nov 23, 2015

Best Answer 

 #1
avatar+105606 
+10

i^61

 

\(i^{61} = i^{60}\times i\\ = (i^{4})^{15} \times i\\ = [(i^2)^2]^{15} \times i\\ = [(-1)^2]^{15} \times i\\ = [1]^{15} \times i\\ = 1\times i\\ =i\)

.
 Nov 23, 2015
 #1
avatar+105606 
+10
Best Answer

i^61

 

\(i^{61} = i^{60}\times i\\ = (i^{4})^{15} \times i\\ = [(i^2)^2]^{15} \times i\\ = [(-1)^2]^{15} \times i\\ = [1]^{15} \times i\\ = 1\times i\\ =i\)

Melody Nov 23, 2015
 #2
avatar+104793 
+10

Thanks, Melody for that answer....

 

Here's another way to evalute this for    i    raised to any  "n"   positve integer

 

n mod 4  =  1    →   i

 

n mod 4  =  2   →   -1

 

n mod 4  = 3   →   - i

 

n mod 4  = 4   →    1

 

So

 

i^61  =      61 mod 4   = 1    →   i            just as Melody found   !!!

 

 

 

cool cool cool

 Nov 23, 2015
edited by CPhill  Nov 23, 2015

13 Online Users