What is the answer to ix=x^2-2x+2 ?

The answer to ix=x^2-2x+2 is x=0.58120…-0.69389…i,x=1.41879…+1.69389…i

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ix=x^2-2x+2

i x = x^{2} - 2 x + 2

x = 0.58120 \dots - 0.69389 \dots i, x = 1.41879 \dots + 1.69389 \dots i

Solution steps

i x = x^{2} - 2 x + 2

Substitute

x = a + bi

i (a + bi) = (a + bi)^{2} - 2 (a + bi) + 2

Expand

- b + ia = (a^{2} - b^{2} - 2 a + 2) + i (- 2 b + 2 ab)

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

[- b = a^{2} - b^{2} - 2 a + 2 a = - 2 b + 2 ab]

[- b = a^{2} - b^{2} - 2 a + 2 a = - 2 b + 2 ab] : (a = 0.58120 \dots, a = 1.41879 \dots, b = - 0.69389 \dots b = 1.69389 \dots)

Substitute back

x = a + bi

x = 0.58120 \dots - 0.69389 \dots i, x = 1.41879 \dots + 1.69389 \dots i

x^{2} + 2 x i + 1 = 0

(2 + i) 2 = c + d i

v = \frac{2 r}{i}

(x - y i)^{2} = 9 (x + y i)

\frac{2 + i}{1 + i} = a + bi

What is the answer to ix=x^2-2x+2 ?
The answer to ix=x^2-2x+2 is x=0.58120…-0.69389…i,x=1.41879…+1.69389…i