What is the answer to i(x)=2000x-2x^2 ?

The answer to i(x)=2000x-2x^2 is x=0,x=1000-1/2 i

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i(x)=2000x-2x^2

i (x) = 2000 x - 2 x^{2}

x = 0, x = 1000 - \frac{1}{2} i

Solution steps

i (x) = 2000 x - 2 x^{2}

Substitute

x = a + bi

i (a + bi) = 2000 (a + bi) - 2 (a + bi)^{2}

Expand

- b + ia = (2000 a - 2 a^{2} + 2 b^{2}) + i (2000 b - 4 ab)

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

[- b = 2000 a - 2 a^{2} + 2 b^{2} a = 2000 b - 4 ab]

[- b = 2000 a - 2 a^{2} + 2 b^{2} a = 2000 b - 4 ab] : (a = 0.00000 \dots, a = 1000, b = 0 b = - \frac{1}{2})

Substitute back

x = a + bi

x = 0, x = 1000 - \frac{1}{2} i

r = \frac{v}{i}

z^{2} (3 - i) + 5 (1 - i) z + 2 + 16 i = 0

z^{2} = - 5 + i

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

\frac{3}{x - y i} = \frac{1 + i}{2 - i}

What is the answer to i(x)=2000x-2x^2 ?
The answer to i(x)=2000x-2x^2 is x=0,x=1000-1/2 i