+0

# got confused :(

0
702
2
+4

what is the sum of i^2017 , i ^2018 , and i ^2019 where i = square root of -1?

Nov 5, 2020

#1
+112504
+2

Just look for the pattern

$$i^1=i\\ i^2=-1\\ i^3=-1i\\ i^4=+1\\ i^5=i\\ \text{and so the pattern starts over.}$$

Nov 5, 2020
#2
+25640
+3

what is the sum of $$i^{2017}$$ , $$i ^{2018}$$ , and $$i ^{2019}$$ where i = square root of -1?

$$Formula: \boxed{\mathbf{i^n+i^{2+n}=0}}$$

$$\begin{array}{|rcll|} \hline && i^{2017}+i^{2018}+i^{2019} \\ &=& i^{2017}+i^{2019}+i^{2018} \quad | \quad \mathbf{i^{2017}+i^{2019} = 0} \\ &=& 0 + i^{2018} \\ &=& i^{2*1009} \\ &=& \left(i^{2}\right)^{1009} \quad | \quad \mathbf{i^2 = -1} \\ &=& \left(-1\right)^{1009} \\ &=& \mathbf{-1} \\ \hline \end{array}$$

Nov 5, 2020