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Find |(223i)3|.

 Aug 15, 2019
 #1
avatar+6251 
+2

The easiest way to go about this is to convert the number to polar form223i=2(1+3i)=22(12+32i)=4(cos(π3)+isin(π3))=4eiπeiπ3=4ei4π3

 

(4ei4π3)3=43e3(i4π3)=64ei4π=64

 

|64|=64

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 Aug 15, 2019
edited by Rom  Aug 15, 2019
edited by Rom  Aug 15, 2019
 #2
avatar
+1

OK here is hopefully the correct answer.

 

(2)33(2)223i+3(2)(23i)2(23i)3=

(2)33(2)223i32(23i)2(23i)3=

8(2)2323i32(23i)2(23i)3=

3(2)223i=

22323i=

243i=

8+72=

64

 

Because you are looking for the absulate value the answer is 

64.

 Aug 15, 2019
 #3
avatar+142 
+3

Another way would be to evaluate |22i3|3. We have: (2)2+(23)2=4+43=16=443=64  

 Aug 15, 2019

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