+0  
 
0
190
1
avatar

What are the fourth roots of 2√3−2i ? Enter the roots in order of increasing angle measure.

 

___cis(___)

 

___cis(___)

 

___cis(___)

 

___cis(___)

 May 14, 2020
 #1
avatar+21955 
0

Transform a + b·i  into r·cis(theta) form.     

 

r  =  sqrt( a2 + b2 )  =  sqrt[ ( 2sqrt(3) )2 + (-2)2 ]  =  sqrt[ 12 + 4 ]  =  4

theta  =  tan-1( b/a )  =  tan-1( -2 / ( 2sqrt(3) ) )  =  -300  =  330o

 

4 cis( 330o )

 

To find the fourth root find the fourth root of the constant and divide the angle by 4.

 41/4 cis( 330o / 4 )  =  sqrt(2)·cis( 82.5o )

 

To find the other three roots, add 90o to the preceding root:  sqrt(2)·cis( 172.5o ), ...

 May 14, 2020

9 Online Users

avatar
avatar