What is the answer to 2(y+i)=y^2 ?

The answer to 2(y+i)=y^2 is y=-0.27201…-0.78615…i,y=2.27201…+0.78615…i

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2(y+i)=y^2

2 (y + i) = y^{2}

y = - 0.27201 \dots - 0.78615 \dots i, y = 2.27201 \dots + 0.78615 \dots i

Solution steps

2 (y + i) = y^{2}

Substitute

y = x + v i

2 (x + v i + i) = (x + v i)^{2}

Expand

2 x + i (2 + 2 v) = (x^{2} - v^{2}) + 2 i xv

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

[2 x = x^{2} - v^{2} 2 + 2 v = 2 xv]

[2 x = x^{2} - v^{2} 2 + 2 v = 2 xv] : (x = - 0.27201 \dots, x = 2.27201 \dots, v = - 0.78615 \dots v = 0.78615 \dots)

Substitute back

y = x + v i

y = - 0.27201 \dots - 0.78615 \dots i, y = 2.27201 \dots + 0.78615 \dots i

i (x) = - \frac{x ^{2}}{4} + 3450 x

(x - i) (x + i) = 0

x + y \cdot i = i

\frac{x}{1 + i} + \frac{y}{1 - 2 i} = 1

x, x^{2} y + sin (y) = 2 π

What is the answer to 2(y+i)=y^2 ?
The answer to 2(y+i)=y^2 is y=-0.27201…-0.78615…i,y=2.27201…+0.78615…i