What is the answer to i(t)=t^2-5t+6 ?

The answer to i(t)=t^2-5t+6 is t=1.38196…-0.61803…i,t=3.61803…+1.61803…i

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i(t)=t^2-5t+6

i (t) = t^{2} - 5 t + 6

t = 1.38196 \dots - 0.61803 \dots i, t = 3.61803 \dots + 1.61803 \dots i

Solution steps

i (t) = t^{2} - 5 t + 6

Substitute

t = x + y i

i (x + y i) = (x + y i)^{2} - 5 (x + y i) + 6

Expand

- y + i x = (x^{2} - y^{2} - 5 x + 6) + i (- 5 y + 2 x y)

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

[- y = x^{2} - y^{2} - 5 x + 6 x = - 5 y + 2 x y]

[- y = x^{2} - y^{2} - 5 x + 6 x = - 5 y + 2 x y] : (x = 1.38196 \dots, x = 3.61803 \dots, y = - 0.61803 \dots y = 1.61803 \dots)

Substitute back

t = x + y i

t = 1.38196 \dots - 0.61803 \dots i, t = 3.61803 \dots + 1.61803 \dots i

x = 0 + i y - 2 x + 2 i y + 7 - 6 i

(x + i y)^{2} - 2 (x - i y) = 0

2 i x + 2 y = 1

p = v i

(a - 2) + (b + 1) i = 8 + 5 i

What is the answer to i(t)=t^2-5t+6 ?
The answer to i(t)=t^2-5t+6 is t=1.38196…-0.61803…i,t=3.61803…+1.61803…i