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Compute $i^{1234}$.

 Jun 19, 2019
 #1
avatar+104688 
+3

Note the repeating pattern

 

i^1  = i

i^2  = -1

i^3  =  -i

i^4  = 1

 

So....divide 1234 by 4  and we have

 

308. 5  =  308 + 1/2    =   308 + 2/4

 

The "2"  tells us that  i^1234 is equivalent to  i^2  =   -1

 

 

cool cool cool

 Jun 19, 2019
 #2
avatar+23273 
+3

Compute \(\mathbf{i^{1234}}\).

 

\(\begin{array}{|rcll|} \hline && \mathbf{i^{1234}} \\ &=& \left(i^2\right)^{617} \quad | \quad i^2 = -1 \\ &=& \left(-1\right)^{617} \\ &=& \mathbf{ -1} \\ \hline \end{array} \)

 

laugh

 Jun 19, 2019

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