What is the answer to iz^2-2z=2i ?

The answer to iz^2-2z=2i is z=1-i,z=-1-i

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iz^2-2z=2i

i z^{2} - 2 z = 2 i

z = 1 - i, z = - 1 - i

Solution steps

i z^{2} - 2 z = 2 i

Substitute

z = x + y i

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

Expand

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

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

Rewrite

2 i

in standard complex form:

0 + 2 i

(- 2 x y - 2 x) + i (x^{2} - y^{2} - 2 y) = 0 + 2 i

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

[- 2 x y - 2 x = 0 x^{2} - y^{2} - 2 y = 2]

[- 2 x y - 2 x = 0 x^{2} - y^{2} - 2 y = 2] : (x = 1, x = - 1, y = - 1 y = - 1)

Substitute back

z = x + y i

z = 1 - i, z = - 1 - i

8 x^{2} + 9 x + i = 0

\frac{3 b - 2 ai}{4 - 3 i} = 0

5 + (5 x + y) i = 5 x - 2 i

∣ z ∣ + z = 2 + i

z^{2} = \frac{1 + i 3}{2}