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

The answer to i(x)=-x^2+60x is x=0,x=60-i

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

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

x = 0, x = 60 - i

Solution steps

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

Substitute

x = a + bi

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

Expand

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

[- b = - a^{2} + b^{2} + 60 a a = 60 b - 2 ab] : (a = 0, a = 60, b = 0 b = - 1)

Substitute back

x = a + bi

x = 0, x = 60 - i

m, (m - n)^{2} = - 2 i

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

k_{1} - 3 - 27 i k_{2} = 0

c, i = \frac{d}{( 1 - c )}

(a + i)^{2} = 8 + bi