Question 1201844
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Use deMoivre's Theorem.<br>
{{{(z+1)^4=1-i=sqrt(2)*cis(7pi/4)=(2^(1/2))*cis(7pi/4)}}}<br>
The "primary" 4th root of that expression is<br>
{{{z+1=(2^(1/8))*cis(7pi/16)}}}<br>
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:<br>
{{{z+1=(2^(1/8))*cis(15pi/16)}}}
{{{z+1=(2^(1/8))*cis(23pi/16)}}}
{{{z+1=(2^(1/8))*cis(31pi/16)}}}<br>
Subtract 1 from each of those expressions to find the values of z....<br>