What is the answer to i(t)=4t^2-48t+154 ?

The answer to i(t)=4t^2-48t+154 is t=5.54543…-1.52492…i,t=6.45456…+1.77492…i

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i(t)=4t^2-48t+154

i (t) = 4 t^{2} - 48 t + 154

t = 5.54543 \dots - 1.52492 \dots i, t = 6.45456 \dots + 1.77492 \dots i

Solution steps

i (t) = 4 t^{2} - 48 t + 154

Substitute

t = x + y i

i (x + y i) = 4 (x + y i)^{2} - 48 (x + y i) + 154

Expand

- y + i x = (4 x^{2} - 4 y^{2} - 48 x + 154) + i (- 48 y + 8 x y)

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

[- y = 4 x^{2} - 4 y^{2} - 48 x + 154 x = - 48 y + 8 x y]

[- y = 4 x^{2} - 4 y^{2} - 48 x + 154 x = - 48 y + 8 x y] : (x = 5.54543 \dots, x = 6.45456 \dots, y = - 1.52492 \dots y = 1.77492 \dots)

Substitute back

t = x + y i

t = 5.54543 \dots - 1.52492 \dots i, t = 6.45456 \dots + 1.77492 \dots i

i (t) = 8 t^{2} - 4 t A

z^{2} - 2 (1 + i) z + i = 0

∣ z + i ∣ = 3 + 0 i

x^{2} - 3 (1 - i) x - 5 i = 0

\frac{( x - 1 )}{2 - x} = i

What is the answer to i(t)=4t^2-48t+154 ?
The answer to i(t)=4t^2-48t+154 is t=5.54543…-1.52492…i,t=6.45456…+1.77492…i