What is the answer to i(t)=3t^2-t ?

The answer to i(t)=3t^2-t is t=0,t= 1/3+1/3 i

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i(t)=3t^2-t

i (t) = 3 t^{2} - t

t = 0, t = \frac{1}{3} + \frac{1}{3} i

Solution steps

i (t) = 3 t^{2} - t

Substitute

t = x + y i

i (x + y i) = 3 (x + y i)^{2} - (x + y i)

Expand

- y + i x = (3 x^{2} - 3 y^{2} - x) + i (- y + 6 x y)

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

[- y = 3 x^{2} - 3 y^{2} - x x = - y + 6 x y]

[- y = 3 x^{2} - 3 y^{2} - x x = - y + 6 x y] : (x = 0, x = \frac{1}{3}, y = 0 y = \frac{1}{3})

Substitute back

t = x + y i

t = 0, t = \frac{1}{3} + \frac{1}{3} i

x, z = (x^{2} - 1) + (x - 1) i

(a - 2) + (b + 1) i = 6 + 5 i

(1 + i) (a + bi) + 5 = 2 - 3 i

x + i y = x^{2} + y^{2}

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

What is the answer to i(t)=3t^2-t ?
The answer to i(t)=3t^2-t is t=0,t= 1/3+1/3 i