What are the solutions to the equation z^4=289 ?

The solutions to the equation z^4=289 are z=sqrt(17),z=-sqrt(17),z=sqrt(17)i,z=-sqrt(17)i

Find the zeros of z^4=289

The zeros of z^4=289 are z=sqrt(17),z=-sqrt(17),z=sqrt(17)i,z=-sqrt(17)i

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z^{4} = 289

z = 17, z = - 17, z = 17 i, z = - 17 i

Solution steps

z^{4} = 289

Rewrite the equation with

u = z^{2}

and

u^{2} = z^{4}

u^{2} = 289

Solve

u^{2} = 289 : u = 289, u = - 289

u = 289, u = - 289

Substitute back

u = z^{2},

solve for

z

Solve

z^{2} = 289 : z = 17, z = - 17

Solve

z^{2} = - 289 : z = 17 i, z = - 17 i

The solutions are

z = 17, z = - 17, z = 17 i, z = - 17 i

1157

12 - 11 x - x^{2}

x^{2} - x + 1 < 0

(x - 4) (- 5 x + 1) = 0

0 = x^{2} + 5 x + 6

What are the solutions to the equation z^4=289 ?
The solutions to the equation z^4=289 are z=sqrt(17),z=-sqrt(17),z=sqrt(17)i,z=-sqrt(17)i
Find the zeros of z^4=289
The zeros of z^4=289 are z=sqrt(17),z=-sqrt(17),z=sqrt(17)i,z=-sqrt(17)i