I understand where 3pi4 came from but not 11pi4 and the numb

I understand where 3pi/4 came from, but not 11pi/4 and the numbers after.

Where did 11 pi/4come from? How was it solved from 3pi/4? Looks like 8 was added, but why? If we plot the complex number 2i-2 (that is x= -2 and y = 2) in the complex plane; the polar r = 2squareroot 2, and theta = 3pr/4, or 11 pi/4, 19 pi/4, 27 pi/4,...etc. We know that From equation (1), Z = r R that is, to find the polar coordinates of the cube root of a number, we find the cube root of rand divide the angle by 3. Then the polar coordinates of 3squareroot 2i - 2 are r = squareroor 2, theta = 3pi/12, 11pi/12, 19pppi/12, 27pi/1,... = pi/4,11pi/12,19pi/12,9pi/4,...

Solution

for z =-2+2i

3/4 is co terminal with 2 +(3/4) ,4+(3/4),6+(3/4),................

=3/4,2 +(3/4) ,4+(3/4),6+(3/4),................

=3/4,(8 +3)/4 ,(16+3)/4,(24+3)/4),................

=3/4,(11/4) ,(19/4),(27/4),................