Equation z4 +z3 +z−1 = 0 can be written after re-arranging the terms
=> (z4-1) +z(z2+1)=0
=> (z2-1)(z2+1)+z(z2+1)=0
=> (z2+1) (z2+z-1) =0
=> So roots of z2 +1 =0 are -i and i;
roots of (z2 +z-1) =0 are (−1+5)/2(-1+\sqrt{\smash[b]{5}})/2(−1+5)/2 and (−1−5)/2(-1-\sqrt{\smash[b]{5}})/2(−1−5)/2.
hence other 3 roots are -i, (−1+5)/2(-1+\sqrt{\smash[b]{5}})/2(−1+5)/2 and (−1−5)/2(-1-\sqrt{\smash[b]{5}})/2(−1−5)/2 .
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments
Leave a comment