What is the answer to z^2=|z|+2 ?

The answer to z^2=|z|+2 is z=-2\lor z=2

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z^2=|z|+2

z^{2} = ∣ z ∣ + 2

z = - 2 or z = 2

Solution steps

z^{2} = ∣ z ∣ + 2

Find positive and negative intervals

z < 0, z \geq 0

Solve the inequality for each interval

z = - 2 or z = 2

∣ 8 x - 1 ∣ - 8 = - 16

\frac{- 2 x}{3} + 2 = 3

3 - \frac{3}{2} x + 8 + 9 = 24

5 = 3 \frac{1}{2} y - 4 - 7

18 - 3 x - x^{2} = 3 - x