What is the answer to z^2=2zi ?

The answer to z^2=2zi is z=0,z=2i

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z^2=2zi

z^{2} = 2 z i

z = 0, z = 2 i

Solution steps

z^{2} = 2 z i

Substitute

z = x + y i

(x + y i)^{2} = 2 (x + y i) i

Expand

(x^{2} - y^{2}) + 2 i x y = - 2 y + 2 i x

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[x^{2} - y^{2} = - 2 y 2 x y = 2 x]

[x^{2} - y^{2} = - 2 y 2 x y = 2 x] : (x = 0, x = 0, y = 0 y = 2)

Substitute back

z = x + y i

z = 0, z = 2 i

(x + y i) - (- 6 + 14 i) = 18 + 2 i

(6 i)^{2} + x^{2} = 100

y^{2} + y^{2} i + 6 + i = 2 x + i x

z^{2} - 5 + 12 i = 0

x, y sin (y) - 2 - 5 x^{2} = 0