SOLUTION: (z+1)^4=1-i

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Question 1201844: (z+1)^4=1-i
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use deMoivre's Theorem.

%28z%2B1%29%5E4=1-i=sqrt%282%29%2Acis%287pi%2F4%29=%282%5E%281%2F2%29%29%2Acis%287pi%2F4%29

The "primary" 4th root of that expression is

z%2B1=%282%5E%281%2F8%29%29%2Acis%287pi%2F16%29

The other 4th roots of the expression have the same magnitude and are spaced around the Argand plane at intervals of (2pi)/4 = pi/2 radians:

z%2B1=%282%5E%281%2F8%29%29%2Acis%2815pi%2F16%29
z%2B1=%282%5E%281%2F8%29%29%2Acis%2823pi%2F16%29
z%2B1=%282%5E%281%2F8%29%29%2Acis%2831pi%2F16%29

Subtract 1 from each of those expressions to find the values of z....