What is the answer to i(x)=-100x^2+1000x+7500 ?

The answer to i(x)=-100x^2+1000x+7500 is No Solution

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i(x)=-100x^2+1000x+7500

i (x) = - 100 x^{2} + 1000 x + 7500

No Solution

Solution steps

i (x) = - 100 x^{2} + 1000 x + 7500

Substitute

x = a + bi

i (a + bi) = - 100 (a + bi)^{2} + 1000 (a + bi) + 7500

Expand

- b + ia = (- 100 a^{2} + 100 b^{2} + 1000 a + 7500) + i (1000 b - 200 ab)

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

[- b = - 100 a^{2} + 100 b^{2} + 1000 a + 7500 a = 1000 b - 200 ab]

[- b = - 100 a^{2} + 100 b^{2} + 1000 a + 7500 a = 1000 b - 200 ab] : No Solution

Substitute back

x = a + bi

No Solution

- w^{2} + 9 i w + 20 = 0

(a + bi)^{2} - (a + bi) + i (a - bi) = 0

3 x + 21 i = 6 + 7

\frac{1 + ai}{6 + bi} = 3 + 7 i

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

What is the answer to i(x)=-100x^2+1000x+7500 ?
The answer to i(x)=-100x^2+1000x+7500 is No Solution