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Question

Find the roots of (4+4i)pq . Where p and q are integers and q 0



Your Answer
A

  Where n = 0,1,2,3,..........q-1

Your Answer
B

 Where n = 0,1,2,3,..........q-1

Your Answer
C

Where n = 0,1,2,3,..........q-1

Correct Answer
D

 Where n = 0,1,2,3,..........q-1


Solution

The correct option is D

 Where n = 0,1,2,3,..........q-1


Let z = 4+4i

|z| = 4 2

arg(z) = tan1 (44)π4

Express of Z in polar form 

z = 42 (cosπ4+isinπ4)
zpq = (42)pq [cosπ4+isinπ4]pq

= (42)pq [cospq(2nπ+π4)+isinpq(2nπ+π4)]

Where n = 0,1,2,3,..........q-1

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