There are 4 solutions and they are:
z = sqrt(17)
z = -sqrt(17)
z = i*sqrt(17)
z = -i*sqrt(17)
where i = sqrt(-1) and also "sqrt" is shorthand for "square root"
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Work Shown:
Let x = z^2. Square both sides to get x^2 = (z^2)^2 = z^(2*2) = z^4
In short, x^2 = z^4, so we can replace the 'z^4' with 'x^2' to get this new equation x^2 = 289
Apply the square root to both sides
x^2 = 289
sqrt(x^2) = sqrt(289)
sqrt(x^2) = sqrt(17^2)
|x| = 17
x = 17 or x = -17
For each equation above, replace x with z^2 and solve that equation for z
x = 17
z^2 = 17
sqrt(z^2) = sqrt(17)
|z| = sqrt(17)
z = sqrt(17) or z = -sqrt(17)
which are two solutions out of the four total
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The other two solutions are found by plugging x = z^2 into x = -17 and solving for z
x = -17
z^2 = -17
sqrt(z^2) = sqrt(-17)
|z| = sqrt(-1*17)
|z| = sqrt(-1)*sqrt(17)
|z| = i*sqrt(17)
z = i*sqrt(17) or z = -i*sqrt(17)
which are the other two solutions