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Find (1+i2)46. Any help is appreciated! Thanks!

 Aug 29, 2018
 #1
avatar+818 
+1

In  , we can apply exponent rule,  . If we do it here, we will get:  .

 Aug 30, 2018
 #2
avatar+9488 
+3

Find   .

 

Let's convert  1 + i  to polar form so we can use de Moivre's Theorem.

 

 

Now lets raise both sides of that equation to the power of  46 .

 

 

And divide both sides by 

 

 

De Moivre's Theorem says....

 

    So....

 

 

Now let's find a reference angle that is coterminal with    by subtracting    five times.

 

 

So....

 

 Aug 30, 2018
 #3
avatar+26398 
+7

Find

\left(\frac{1+i}{\sqrt{2}}\right)^{46}.

 

 

laugh

 Aug 30, 2018

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