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
93
1
avatar

Evaluate $i^{11} + i^{111}$.

 Jun 20, 2019
 #1
avatar+103069 
+1

i^11 + i^111

 

Here's another method you might find easier :

 

Note i^2  = -1

 

i^11  =  i^10 * i   =  (  i^2 )^5  * i   =  (-1)^5 * i

And  - 1 raised to an odd power = -1

So....we have    (-1) * i   = - i

 

Likewise

 

i^111  =  i^110 * i   =   (i^2)^55 * i  =  (-1)^55 * i   =  -1 * i  =  -i

 

So

 

i^11 + i^111  =

 

-i  + -i  =

 

-2i

 

 

cool cool cool

 Jun 20, 2019

53 Online Users

avatar