What is the answer to i(q)=30q-0.3q^2 ?

The answer to i(q)=30q-0.3q^2 is q=0,q=100-10/3 i

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i(q)=30q-0.3q^2

i (q) = 30 q - 0.3 q^{2}

q = 0, q = 100 - \frac{10}{3} i

Solution steps

i (q) = 30 q - 0.3 q^{2}

Substitute

q = x + y i

i (x + y i) = 30 (x + y i) - 0.3 (x + y i)^{2}

Expand

- y + i x = (30 x - 0.3 x^{2} + 0.3 y^{2}) + i (30 y - 0.6 x y)

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

[- y = 30 x - 0.3 x^{2} + 0.3 y^{2} x = 30 y - 0.6 x y]

[- y = 30 x - 0.3 x^{2} + 0.3 y^{2} x = 30 y - 0.6 x y] : (x = 0.00000 \dots, x = 100, y = 0 y = - \frac{10}{3})

Substitute back

q = x + y i

q = 0, q = 100 - \frac{10}{3} i

r i = - \frac{10}{16} q + \frac{5}{2}

(z - 2)^{2} - 2 i^{2} = 0

a + 3 + 2 bi = 5 - 4 i

0 = 1 0^{5} (10 + i x) (1000 + i x)

- x^{2} = 2 i

What is the answer to i(q)=30q-0.3q^2 ?
The answer to i(q)=30q-0.3q^2 is q=0,q=100-10/3 i