What is the answer to i(x)=60x-0.01x^2 ?

The answer to i(x)=60x-0.01x^2 is x=0,x=6000-100i

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i(x)=60x-0.01x^2

i (x) = 60 x - 0.01 x^{2}

x = 0, x = 6000 - 100 i

Solution steps

i (x) = 60 x - 0.01 x^{2}

Substitute

x = a + bi

i (a + bi) = 60 (a + bi) - 0.01 (a + bi)^{2}

Expand

- b + ia = (60 a - 0.01 a^{2} + 0.01 b^{2}) + i (60 b - 0.02 ab)

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

[- b = 60 a - 0.01 a^{2} + 0.01 b^{2} a = 60 b - 0.02 ab]

[- b = 60 a - 0.01 a^{2} + 0.01 b^{2} a = 60 b - 0.02 ab] : (a = 0, a = 6000, b = 0 b = - 100)

Substitute back

x = a + bi

x = 0, x = 6000 - 100 i

- 340 i = X (10 - 159 i) - Y (- 159 i)

7 x + 2 y - 2 i = 3 + (3 x + \frac{1}{5} y) i

ai + b + 4 = bi - 2 i + 3 a

z^{2} = 8 + 6 i

(2 x - 3 y - 5) + i (x + 2 y + 1) = 0

What is the answer to i(x)=60x-0.01x^2 ?
The answer to i(x)=60x-0.01x^2 is x=0,x=6000-100i