SOLUTION: find all complex numbers which satisfy z^5+4z=0 and express your answer in cartesian form?

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Question 806536: find all complex numbers which satisfy z^5+4z=0 and express your answer in cartesian form?
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!

                        z5 + 4z = 0

                      z(z4 + 1) = 0

          z(z4 + 1 + 4z2 - 4z2) = 0

          z(z4 + 4z2 + 1 - 4z2) = 0

        z[(z4 + 4z2 + 1) - 4z2] = 0

             z[(z2 + 1)2 - 4z2] = 0

z[(z2 + 1) - 2z][(z2 + 1) + 2z] = 0

    z[z2 + 1 - 2z][z2 + 1 + 2z] = 0

    z(z2 - 2z + 1)(z2 + 2z + 1) = 0

z = 0;  z2 - 2z + 1 = 0;  z2 + 2z + 1 = 0

Solve the quadratics by the quadratic formula and get

z = 0; z = 1 + 1; z = 1 - i; z = -1 + i;  z = -1 - i

Edwin
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