+0  
 
0
39
3
avatar

Evaluate (5+5sqrt(3)i)^7 using DeMoivre’s theorem.

Write your answer in rectangular form. Show all your work.

 May 14, 2020
 #1
avatar+20906 
0

First, place the problem in r·cis(theta) form.

 

  r  =  sqrt( x2 + y2 )  =  sqrt[ (5)2 + (5·sqt(3))2 ]  =  sqrt( 25 + 75 )  =  sqrt(100)  =  10

 

  theta  =  tan-1( y / x )  =  tan-1( 5·sqt(3) / 5 )  =  60o

 

[ 10·cis( 60o) ]7  =  107 · cis( 7·60o )  =  ...

 May 14, 2020
 #2
avatar
0

Is this the answer?

5000000+5000000isqrt(3)

Guest May 14, 2020
 #3
avatar+44 
0

was that the answer.

jscare  May 22, 2020

15 Online Users

avatar
avatar