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Did I do these right??

 

1.

 

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2.

What are the solutions to x^3=−2−2i in polar form?

 May 16, 2020
 #1
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Problem #1:  you handled the constants correctly; however, the angles should be subtracted, not divided.

 May 16, 2020
 #2
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Problem #2:  r  =  sqrt( (-2)2 + (-2)2 )  =  sqrt( 4 + 4 )  =  sqrt(8)

 

angle  =  tan-1( -2 / -2 )  =  tan-1( 1 )      =  5pi/4

 

To find the primary cube root, find the cube root of the r value and divide the angle by 3.

To find the next cube root, the r value remains the same but you need to add 2pi/3 to the angle.

To find the last cube root, the r value remains the same but you need to add another 2pi/3 to the angle.

 May 16, 2020

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